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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Extensions · GroupsCore.jl</title><link rel="canonical" href="https://kalmarek.github.io/GroupsCore.jl/extensions/"/><link href="https://fonts.googleapis.com/css?family=Lato|Roboto+Mono" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.0/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.0/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.0/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.11.1/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit">GroupsCore.jl</span></div><form class="docs-search" action="../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../">GroupsCore</a></li><li><span class="tocitem">Basic interface</span><ul><li><a class="tocitem" href="../groups/">Groups</a></li><li><a class="tocitem" href="../group_elements/">Group elements</a></li></ul></li><li class="is-active"><a class="tocitem" href>Extensions</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Extensions</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Extensions</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/kalmarek/GroupsCore.jl/blob/master/docs/src/extensions.md#" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="Extensions"><a class="docs-heading-anchor" href="#Extensions">Extensions</a><a id="Extensions-1"></a><a class="docs-heading-anchor-permalink" href="#Extensions" title="Permalink"></a></h1><p>The following functions are defined in <code>GroupsCore</code> only to be extended externally:</p><pre><code class="language-julia">isabelian
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Extensions · GroupsCore.jl</title><link rel="canonical" href="https://kalmarek.github.io/GroupsCore.jl/extensions/"/><link href="https://fonts.googleapis.com/css?family=Lato|Roboto+Mono" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.0/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.0/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.0/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.11.1/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit">GroupsCore.jl</span></div><form class="docs-search" action="../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../">GroupsCore</a></li><li><span class="tocitem">Basic interface</span><ul><li><a class="tocitem" href="../groups/">Groups</a></li><li><a class="tocitem" href="../group_elements/">Group elements</a></li></ul></li><li class="is-active"><a class="tocitem" href>Extensions</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Extensions</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Extensions</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/kalmarek/GroupsCore.jl/blob/master/docs/src/extensions.md#" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="Extensions"><a class="docs-heading-anchor" href="#Extensions">Extensions</a><a id="Extensions-1"></a><a class="docs-heading-anchor-permalink" href="#Extensions" title="Permalink"></a></h1><p>The following (empty) functions are defined in <code>GroupsCore</code> only to be extended externally:</p><pre><code class="language-julia">isabelian
issolvable
isnilpotent
isperfect
Expand All @@ -10,4 +10,4 @@
centralizer
normalizer
stabilizer
right_coset_representatives</code></pre><article class="docstring"><header><a class="docstring-binding" id="GroupsCore.index" href="#GroupsCore.index"><code>GroupsCore.index</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia">index(H::Gr, G::Gr) where {Gr &lt;: Group}</code></pre><p>Return the index <span>$|G : H|$</span>, where <span>$H \subseteq G$</span>. If <span>$H$</span> is not contained in <span>$G$</span>, an error is thrown.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/kalmarek/GroupsCore.jl/blob/2e536fcff45000b6304a5c41b993b1d26db000b0/src/extensions.jl#L17">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="GroupsCore.left_coset_representatives" href="#GroupsCore.left_coset_representatives"><code>GroupsCore.left_coset_representatives</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia">left_coset_representatives(H::Gr, G::Gr) where {Gr &lt;: Group}</code></pre><p>Return representatives of the left cosets <span>$h G$</span> where <span>$h$</span> are elements of <span>$H$</span>. If <span>$H$</span> is not contained in <span>$G$</span>, an error is thrown.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/kalmarek/GroupsCore.jl/blob/2e536fcff45000b6304a5c41b993b1d26db000b0/src/extensions.jl#L25">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../group_elements/">« Group elements</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Monday 11 December 2023 15:12">Monday 11 December 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
right_coset_representatives</code></pre><article class="docstring"><header><a class="docstring-binding" id="GroupsCore.index" href="#GroupsCore.index"><code>GroupsCore.index</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia">index(H::Gr, G::Gr) where {Gr &lt;: Group}</code></pre><p>Return the index <code>|G : H|</code>, where <code>H ≤ G</code> is a subgroup. If <code>H</code> is not contained in <code>G</code>, an error is thrown.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/kalmarek/GroupsCore.jl/blob/998e889e4125aeb4abc001a939595e1b17bad0d5/src/extensions.jl#L17-L21">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="GroupsCore.left_coset_representatives" href="#GroupsCore.left_coset_representatives"><code>GroupsCore.left_coset_representatives</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia">left_coset_representatives(H::Gr, G::Gr) where {Gr &lt;: Group}</code></pre><p>Return representatives of the left cosets <code>h G</code> where <code>h</code> are elements of <code>H</code>. If <code>H</code> is not contained in <code>G</code>, an error is thrown.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/kalmarek/GroupsCore.jl/blob/998e889e4125aeb4abc001a939595e1b17bad0d5/src/extensions.jl#L24-L28">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../group_elements/">« Group elements</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Monday 11 December 2023 15:15">Monday 11 December 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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