<p>The Groupslibrary accessto groupsof <q>smallq orders. The groups are sorted by their orders and they are listed up to isomorphism; that is, for each of available orders complete irredundant listof isomorphism type of groups given. Currentlythe contains following groups/p
<ul>
<li><p>those of order at most 2000 exceptspanclass"ontSS"< /< classnocss>nbsp;<span<a href="chap1_mj.html#X872991747D5CFD35">.- NumberSmallGroupsAvailable/pan
</li>
<li><p>those of cubefree order span="ContSS">br/< class=">;;/pan>a href=chap1_mjhtmlX83044B9D7E3BDF35"128IdSmallGroup<>/>
</li>
<li><p>those of order<pan="ContSS"><br ><span="nocss>nbsp; .html#X85352440869327EC"121 IdsOfAllSmallGroups/</>
</li>
</ul>
t three in listanexplicit range orders last provide to of having of types
<p>The=" name="">>/>
<pT Small library to groups <q>mall. The are by orders they listed to isomorphism that isfor of the ordersa and irredundant list isomorphismtype of groups isgiven. Currently he contains following groups/
</d>
<dt<strong class"ark>(2)/dt>
<dd><p>the <><p> of orderspan=""\(^\)</span the <spanclassSimpleMath\p =35,,1\<s> class="SimpleMath">\(0 \ 49)</span> groups);</p>
</dd>
<dt><strong class="Mark">(3)</strong></dt>
<dd><p>the remaining groups of order <span class="SimpleMath">\(2^n \cdot
</dd>
<dt><strong class="Mark">(4)</strong></dt>
<dd><p>the remaining groups of order <span class="SimpleMath">\(5^5\)</span>, <span class="SimpleMath">\(7^4\)</span> and of order <span class=
</dd>
<dt><strong class="Mark">(5)</strong></dt>
<dd><p>theremaininggroups of order most 200 except02,112,153 and.</p>
</dd>
<dt><strong class="Mark">(7)</strong/t>
<dd><p>the groups of order 512.</p>
</dd>
<dt><strong classMark>8)/strong/dt>
<dd><p>the groups>Thelibrary organised in1layersEach layercontains groups certain orders andtheir group identification. It is to install firstspan="SimpleMath">\n\</pan of thegroup and the <span classSimpleMath\m)</span> layers the groupidentification foreachspanclass="SimpleMath">(1\leq m \leq\ 11\)<span. might be to save space.There an extensivecodeclass="file"READMEcode file the Groups library in thecodeclass>small/code> ofthe class="pkg"GAPstrong distribution detailed on layersA brief the isherep>
</dd>
<dt><strongjava.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 0 ddtheremaining of < class"">\(^n\<spanspanclass""(\ n leqspan<>
</dd>
<dt><strong class="Mark">(10)</strong></dt>
<dd><p>he groupsof order at 50 000 of squarefree.</p>
</dd>
<dt><strong class="Mark">(11)</strong></dt>
<dd><p>the remaining groups of order
</dd>
</dl>
<p>he in this library been carefully and cross-checked is believed tobe. However no guarantees are givenand should,as, make own checks critical cases/p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SmallGroupsAvailable</code>( <var class="Arg">order</var> )</td><td class="tdright">( function )</td></tr></table></div
<p>returns <code class="code">true</code> if the library of
<
<
<div classdivclass="func>
tr
code=func&27;/> varArg</, <varclassArgi/> </tdclass">( function
/tr
<p>returns groups certainproperties specified byvar="Arg"></varvar"Arg">arg</ar a numberspan="SimpleMath"\(n\)/span>,then function all of order class=SimpleMath">\(n)code<> class/.thisfirst class">Size/> (ahref"..../ref.html#X858ADA3B7A684421">Reference: Size) and the first value an order or a range orders. If value is a it is considered a of possible function values to . The thosegroups of the their .
<p>Precomputed information is stored >
<div class="example"><pre>
s class"gapgt;">AllSmallGroups(6)
[ <pc group
&;pcgroup size 2 generators; ]
<span class="GAPprompt">gap></span> <span class="GAPinput">AllSmallGroups([ (1,,,4,)(,23 ]
[ < group size 0 with generatorsgt
<pc group of size 60 with 4 generators> ]
</prespanclassGAPprompt>></spanspanclass="GAPinput"G =SmallGroup 78, 1000 );</pan>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"<pan="GAPprompt">gapgt;</span <span class="GAPinput">G := SmallGroup [78,10000 )</>
<p>returns one group with certain properties as
"C6"
<span class="GAPprompt">gap></span> <span class="GAPinput">G := OneSmallGroup( 6, IsAbelian, false );</span>
<pc group of size 6 with 2 generators>
<span class="GAPprompt">gap></span> <java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 "S3" spanG>gapgt> span=""G:OneSmallGroup110] ;/>
Group([ (1,2,3,4,5), (1,2,3) ])
</pre></div>
<p><p>eturns groupswith certain as specified <var class"Arg>arg. If >function/odeandcodeclasscode></code> case first function be < classfuncSize</code (a=".././doc/ref/.htmlX858ADA3B7A684421"<span class"">Reference</spana)and value order a oforders valueis then considered of function include function thosegroups the orders those remaining and values>
/table>
<p>eturns thecatalogue of <var="Arg">G<varin thestrong="pkg">GAPstrong3 catalogue of solvable groupsis the returnsa <codeclass"< class="rg</varvar class=">i]Arg">G is isomorphic to the groupSolvableGroup( , GAP >
<1, java.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 11
<div class="example"><pre>
<span class="GAPprompt">gap&<p<a id"X85352440869327EC" nameX85352440869327EC<a<pjava.lang.StringIndexOutOfBoundsException: Range [62, 63) out of bounds for length 62
here 51 groups order 32java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34
They sortedby their.
1 is cyclic.
2 - 20 have rank
21 - 44 have rankdiv classexample<pre>
45 - 50 have rank 4<pan="GAPprompt">><span<span="GAPinput">IdsOfAllSmallGroups( 60,IsNilpotentGroup);/span>
51 is elementary abelian class=GAPprompt>&;</pan =GAPinputIdsOfAllSmallGroups6,IsNilpotentGroupfalse<span
<p><strong class="pkg">GAP</strong> loads all necessary data from the library automatically, but it does not delete the data from the workspace again. Usually, this will be not necessary, since the data is<pre/>
<div class="func"><table class="func" width="100%"java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<If set <code classcode>rue>, then of <span="SimpleMath">(3^7\<span<span="SimpleMath7)/span> \7\<span< =SimpleMath17\)<spanordered ordered version 1. theIf iscode=code"> whichisthedefaultas 4 different ordering that theonein .2,isused The >SMALLGP_PERMcode< class"SimpleMath">(\</span with ="impleMath>\(x=3,5,,11\),give theold index corresponding to a new index .In 11-1. amisunderstoodordering based on theoldorderingandthepermutations spanclass="SimpleMath(2,30)33044305)(,0))span>< class"\(149(14601061(5,0402)) \((733710)472105)(51))/pan were.java.lang.StringIndexOutOfBoundsException: Index 1057 out of bounds for length 1057
<p> </p>
<div class="chlinkprevnextbot"> <a href="chap0_mj.html">[Top of Book class"func"><table="func" width"10"<><td="tdleft>unc2;<code <class">G
Die Informationen auf dieser Webseite wurden
nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit,
noch Qualität der bereit gestellten Informationen zugesichert.
Bemerkung:
Die farbliche Syntaxdarstellung ist noch experimentell.