Add SemidirectDecompositions and enhance/change StructureDescription #763

!!! WARNING !!! This changes the behaviour of StructureDescription compared to the previous state, which was inconsistent with the manual. SemidirectDecompositionsOfFiniteGroup is added. This computes all or some semidirect decompositions of a group. An optional second argument can be given as the normal subgroups for which complements should be sought. Complements for normal subgroups are found by ComplementClassesRepresentatives. Unfortunately, this does not work if both N and G/N are nonsolvable. Further, an optional argument "any" is recognized, when it should return only one nontrivial semidirect decomposition if exists and fail otherwise. This is mostly implemented by applying Schur-Zassenhaus by checking if any nontrivial normal Hall subgroups exist. Another optional argument "str" is recognized, when it does not necessarily compute the complement to the normal subgroup if Schur-Zassenhaus applies. The reason is that computing the complement might be expensive and for StructureDescription only the isomorphism type of the complement is interesting. SemidirectDecompositions is a new attribute, computing all semidirect decompositions. SemidirectFactorsOfGroup is removed completely. It computed all conjugacy classes of all subgroups and therefore was rather inefficient. Further, it did not compute _all_ semidirect decompositions, but only the ones with subgroups having the same size as the first subgroup having a normal complement. This yielded inconsistent behaviour with the manual, the smallest example for such a group was SmallGroup(504,7). StructureDescription now works for infinite abelian groups, as well. Further, for semidirect decompositions it calls SemidirectDecompositionsOfFiniteGroup with "str" argument. NOTE that if the group G has a nonsolvable normal subgroup N such that G/N is nonsolvable, as well, then ComplementClassesRepresentatives errors with "No method found", and thus so do SemidirectDecompositions and StructureDescription. Previously computations for such groups did not error with "No method found", but probably took a long time. gap-system#563 tries to remedy this using the old and inefficient method, however whether it should be merged or not is currently under debate. In the meantime, for such groups we throw an error. StructureDescription of groups having size at most 100 are recomputed, and the manual of StructureDescription is rewritten to match current behaviour. Tests are added. All lines of SemidirectDecompositions are run. Not all lines of StructureDescription are run, some examples for the missing lines should be found later. Tests are aligned with the new behaviour, and not the old one.

This commit adds the old documented behaviour of StructureDescription. If option nice is set, then all SemidirectDecompositions are computed and one [N,H] will be chosen by the old preferences, namely abelian H, abelian N with the most abelian invariants and the most direct factors, and with H acting faithfully on N.

Further, grpnames.g contains the "nice" outputs of StructureDescription.

Now the option short works for infinite abelian groups. Further, it now recognizes nonprimepower duplicates, as well. E.g. the short StructureDescription for the group C6 x C6 is now 6^2.

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Add SemidirectDecompositions and enhance/change StructureDescription #763

Add SemidirectDecompositions and enhance/change StructureDescription #763

Commits on Nov 29, 2016