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<h3>1 <span class="Heading">The <strong class="pkg">lpres</strong> package</java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

<p>This package was written by René Hartung in java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

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<h4>1.1 <span class=

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<p>The Grigorchuk group is not finitely presentable

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<p>where <span class="SimpleMath">\(\sigma\)</span> is the java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

<p>In 2003, Bartholdi <a href="chapBib_mj.html#biBBartholdi03">[Bar03

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<p>where <span class="SimpleMath">\(\Phi^*\java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 0

<p>The <strong class="pkg">lpres</strong>-package defines new <strong class="pkg">GAP</strong> objects to java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

<p>Our nilpotent quotient algorithm generalizes Nickel's algorithm for finitely presented groups (see <a href="chapBib_mj.html#biBNickel96">[Nic96]</a>) which is implemented in the <strong class="pkg">NQ</strong>-package; see <a href="chapBib_mj.html#biBnq">[Nic03]</a>. In difference to the <strong class="pkg">NQ</strong>-package, the <strong class="pkg">lpres</strong>-package is implemented in <strong class="pkg">GAP</strong> only.</p>

<p>Since finite L-presentations generalize finite presentations, our algorithm also applies to finitely presented groups. It coincides with Nickel's algorithm in this special case.</p>

<p>A detailed description of our algorithm can be found in <a href="chapBib_mj.html#biBBEH08">[BEH08]</a> or in the diploma thesis <a href="chapBib_mj.html#biBH08">[Har08]</a>. Furthermore the <strong class="pkg">lpres</strong>-package includes the algorithms of <a href="chapBib_mj.html#biBMR2678952">[Har10]</a> for approximating the Schur multiplier of finitely L-presented groups.</p>

<p>The <strong class="pkg">lpres</strong>-package also includes the Reidemeister-Schreier algorithm from <a href="chapBib_mj.html#biBMR2876891">[Har12]</a>. L-presented groups were introduced as a tool to understand self-similar groups such as the Grigorchuk group. As such, <strong class="pkg">lpres</strong> works in close contact with the package <strong class="pkg">fr</strong>. See <a href="chapBib_mj.html#biBMR3133711">[Har13]</a> for more on the relationships between L-presented groups and self-similar groups.</p>

<p>Finally, we note that we use the term "algorithm" somewhat loosely: many of the algorithms in this package are in fact semi-algorithms, guaranteed to give a correct answer but not guaranteed to terminate.</p>

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