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Improvements to Automorphism group/Group isomorphism (#3783)
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* PERFORMANCE: Automorphism group/Group isomorphism

In particular concerning the calculation of a faithful permutation
representation.

Also `SubgroupConditionAbove` uses composition series
and complement zuppos.

Includes minor addition to `ActionDomain` and required manual/test changes

* ENHANCE: Equality test tools for permutation groups

Add `OrbitsMovedPoints`.
Compare orbits first. If size is know avoid forcing a stabilizer chain if
one group has one.  This helps e.g. when acting on subgroups.

* PERFORMANCE: Direct product structure helps for factor groups

* ENHANCE: Added StructuralSeriesOfGroup

Also added method for trivial closure

* ENHANCE: comparison of classes in pc group

* TEST: Unrelated tests to ensure test ratio does not decrease

As the new code cannot be tested within the time-out limits of travis.
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hulpke authored Jan 18, 2020
1 parent 742ec3a commit d1516f2
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1 change: 1 addition & 0 deletions doc/ref/groups.xml
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Expand Up @@ -421,6 +421,7 @@ the series without destroying the properties of the series.
<#Include Label="AscendingChain">
<#Include Label="IntermediateGroup">
<#Include Label="IntermediateSubgroups">
<#Include Label="StructuralSeriesOfGroup">

</Section>

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2 changes: 1 addition & 1 deletion doc/tut/group.xml
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Expand Up @@ -1181,7 +1181,7 @@ gap> niceaut := NiceObject( aut );
Group([ (1,4,2,3), (1,5,4)(2,6,3), (1,2)(3,4), (3,4)(5,6) ])
gap> IsomorphismGroups( niceaut, SymmetricGroup( 4 ) );
[ (1,4,2,3), (1,5,4)(2,6,3), (1,2)(3,4), (3,4)(5,6) ] ->
[ (1,2,3,4), (1,3,4), (1,3)(2,4), (1,4)(2,3) ]
[ (1,4,3,2), (1,3,2), (1,3)(2,4), (1,2)(3,4) ]
]]></Example>
<P/>
The range of a nice monomorphism is in most cases a permutation group,
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