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<html p>Arguments: <var class="Arg">M</var> -- a path algebra module (<code class="code">PathAlgebraMatModule</code>). <br /></p>
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<div class="chlinktop"><span class="chlink1">Goto Chapterdiv =ejava.lang.StringIndexOutOfBoundsException: Range [20, 19) out of bounds for length 26

<div class="chlinkprevnexttop"> <a href="chap0_mj.html">[Top of Book]</a>   <a href="chap0_mj.html#contents">[Contents]</a>    <a href="chap1_mj.html">[Next Chapter]</a>   </div>

<p id="mathjaxlink" class="<span class="GAPprompt">gap><span><span class="GAPinput">proj := DirectSumProjections(N2);</span>
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<div [ <<[ 6,4 4 ]gt; -g;&[ 3 ,2 ]g&t

<h1>lpres</h1>


<h2>Nilpotent Quotients     , &t<[6 4,4 ]gt; ->< 3,2,2 ]>>

<p>
    1.1.1</p>

<p>
    12 July 2024
  </p>

<     ]
<p><b>
    René Hartung

  </b>
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<p><a id="X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8"></a></p>

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<h3>span classGAPprompt"&;/> <class="APinput> =DirectSumInclusions(2);</>

<div class="ContChap"><a href="chap1_mj.html#X86B8787287B59CA4">1 <span class="Heading">The <strong class="pkg">lpres</strong> package</span></a>
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<div class="ContChap"><a href="chap2_mj.html#X7AEB47327D75B633">2 <span class="Heading">An Introduction to L-presented groups</span></a>
<class=java.lang.StringIndexOutOfBoundsException: Range [21, 20) out of bounds for length 167
</java.lang.StringIndexOutOfBoundsException: Range [7, 6) out of bounds for length 7
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><java.lang.StringIndexOutOfBoundsException: Range [5, 1) out of bounds for length 7
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj<><aid="X7C9BFC678598DBF6" name="X7C9BFC678598DBF6"></a></p>
<span class=<5>421 IsExceptionalModule</5>
<span class="ContSS"><br /><span class="nocss">  </span><a href="java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0
<spanclass"ontSS"<br/<classn">;nbsp;<span><a href="chap2_mj.#81C3537083E40A5C22-4 FreeBurnsideGroup/a</span
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X8796306C7A7924D1">2.2-5 FreeNilpotentGroup</a></span>
<spanclass"ContSS"<br/><pan class=nocss">nbsp </span><a href="chap2_mj.html#X81450ABA81F0FCE5">2.2-6 GeneralizedFabrykowskiGuptaLpGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#java.lang.StringIndexOutOfBoundsException: Index 96 out of bounds for length 0
<java.lang.StringIndexOutOfBoundsException: Range [45, 5) out of bounds for length 146
</div<divjava.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X80B65AF48662DE70">2.3 <span class="Heading">The underlying free group</
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7F883CC57A3CCAC7">2.3-1 java.lang.StringIndexOutOfBoundsException: Index 121 out of bounds for length 0
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X838079A587E8CF43">2.3-2 FreeGeneratorsOfLpGroup</a></span>
<span class="ContSS"><brleModuleh5java.lang.StringIndexOutOfBoundsException: Index 38 out of bounds for length 38
<span class="ContSS"><br /><span class=
<span class="ContSS"><br /><span class="nocss">  </span><a href="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsIndecomposableModule</code>( <var class="Arg">M</var> )</td><td class="tdright">( property )</td></tr></table></div>
</div<div>>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X847047F083826C00">2.4 <span class="Heading">Accessing an L-presentation</span></a>
</>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7CD9BE57815552FF">2.4-1 FixedRelatorsOfLpGroup</a></span>
<<>a id="7E5246D4831DB250" name="X7E5246D4831DB250"></a></p>
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<=">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X85E77B29796AB730">2.pArguments: <arclass=A>M,N</ar> -twopathalgebra  < class""></>.< /</>
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<span <p>Returns: <"java.lang.StringIndexOutOfBoundsException: Range [37, 35) out of bounds for length 132
<"java.lang.StringIndexOutOfBoundsException: Range [20, 19) out of bounds for length 149
java.lang.StringIndexOutOfBoundsException: Range [6, 5) out of bounds for length 153
</<
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X7B5C48EA7CD8A57E">2.6 <span class="Heading">Methods for L-presented groups</span></a>
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<div 
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7C81CB1C7F0D7A90">2.6-1<p>The function   var=A><var>and<var ="rg">N</ar>are<code ="ode">PathAlgebraMatModule</code>s over the same (quotient of a) path algebra.</p>
<span class="ContSS"><br /><span class="
<span class="ContSS"><br />h56424 
<span class="ContSS"><br /><span
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X791C3E5280F38329">3>:<=></ -a java.lang.StringIndexOutOfBoundsException: Range [57, 56) out of bounds for length 124
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<span class="ContSS"><br /><span class<p>: trueif representation varclass"rg"><var is.<p
<span class="ContSS"><br /><span class="java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<<span class""&bsp&bsp;/pan>ahref=".#X8758F663782AE655"3.-3 NqEpimorphismNilpotentQuotient<span>
<
</div></div>
<div class="ContSect"><span <>.4-25 java.lang.StringIndexOutOfBoundsException: Range [30, 28) out of bounds for length 33
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<div class="ContSect"><span class="tocline"><span class="nocss">div class=f"table class=f =""<java.lang.StringIndexOutOfBoundsException: Range [59, 58) out of bounds for length 251
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7E58D47A8729FA8E">3.3-1 InitQuotientSystem</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7910D0698781E02A">3.3-2 ExtendQuotientSystem</a></span>
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<div class="ContSect"<p>Returns: or  <var=Arg>/>and<"Arg"/  isomorphic  not<p
</span>
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<span class="ContSS"><br /><span class="nocss"> 
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7D54126783CB7118"<p>The function first checks if the modules <var class="Arg">M</var> and <var class="Arg">N</var> are modules over the same algebra, and returns fail if not. The function returns true if the modules are isomorphic, otherwise false.<
</<p><a id="8359AC9585777CA1" name"8359C9585777CA1"</><p
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a
</span>
< class=ContSSBlock>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X85F6BC1F8573D710">3.5-1 InfoLPRES</a></span>
<span class="<div class="func"table class="func" width=100<tr><tdclass="dleft"><code class="func">&#8227; IsProjectiveModule</code>( <var class="Arg">M</var> )</td><td class="tdright">( property )</td></tr></table></div>
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<div class="ContChap"><a href="chap4_mj.html#X874D64AA789F224E">4 <span class="Heading">Subgroups of L-presented groups</span></a>
<div class="ContSect"><span class="tocline"><spanp>Returns true  therepresentationvar class=A></>  .</p>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7C82AA387A42DCA0">4.1-1 Subgroup</java.lang.StringIndexOutOfBoundsException: Range [0, 125) out of bounds for length 62
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.htmljava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X7A4EB4E0819ACB91">4.2 <span class="Heading">Computing the index of finite-index subgroups</span></a>
</<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#pan style='color: green'>8227; IsRigidModule</code>( <var class="Arg">M</var> )</td><td class="tdright">( property )<p: java.lang.StringIndexOutOfBoundsException: Range [25, 24) out of bounds for length 124
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<span class="ContSS"><br /><span class=p>  if var class="Arg"M/var>is  rigid ,otherwise./>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X83A0356F839C696F">4.
<="br > =>nbsp;java.lang.StringIndexOutOfBoundsException: Range [59, 58) out of bounds for length 147
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X87A9EC0A7DF04931">4.3 <span class="Heading">
</span>
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<span java.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 0
<java.lang.StringIndexOutOfBoundsException: Range [19, 5) out of bounds for length 146
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<div class="ContChap"><a href="chap5_mj.html#X7FBE94957D7ECCFC">5 <span class="Heading">Approximating the Schur multiplier</span></a>
<div class="ContSect"><span class="tocline"><span class="nocssdiv class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsSemisimpleModule</code>( <var class="Arg">M</var> )</td><td class="tdright">( property )</td></tr></<p>Arguments:<var class=Arg"M/ -apathalgebramodule(codeclass"code"PathAlgebraMatModule>.< >/>
</span>
<div class="ContSSBlock">
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<pan class="ContSS""><r >span class="ocss">&;nbsp;/><href"hap5_mjhtmlX87">5.1-2 FiniteRankSchurMultiplier/>/>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X78084374873BDFE1">5.1-3 EndomorphismsOfFRSchurMultiplier</a></span>
<><span class="nocss">  </span><a href="chap5_mj.html#X7CF92D9880A3687E">5.1-4 EpimorphismCoveringGroups</a></span>
<span class="java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 0
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<div class="ContChap"><a href="chap6_mj.html#X7BC16B0082A2B827">6 <span class="Heading">On a parallel nilpotent quotient algorithm</span></a>
<div class="ContSect"><span class="tocline"<p>: <var class="Arg"M/>- a path  module(codeclass="">PathAlgebraMatModule</>) br<pjava.lang.StringIndexOutOfBoundsException: Index 124 out of bounds for length 124
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<div class=<>Returns:true if the representation <var class="Arg">M</var> is simple.</p>
<div class="ContChap"><a href="chapInd_mj.html"><span class="Heading">Index</span></a></java.lang.StringIndexOutOfBoundsException: Range [0, 91) out of bounds for length 0
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