NonsplitExtension(chr, [vec] )
chr must be a cohomology-record, created by a call of
CHR(G,p,F,mats), where F is a finitely presented group.
If present, vec must be a list of integers of length equal to the
dimension over K = GF(p) of the second cohomology group H^2(G,M) of the
group G in its action on the module M defined by the matrices mats.
NonsplitExtension calculates and returns a presentation of a nonsplit
extension of M by G. Since there may be many such extensions, and
the equivalence classes of these extensions are in one-one correspondence
with the nonzero elements of H^2(G,M), the optional second parameter
can be used to specify an element of H^2(G,M) as a vector.
The default value of this vector is
The set of generators of the finitely presented group that is returned
is a union of two sets, which are in one-one correspondence with the
generators of F and of M (as an abelian group), respectively.
The relators fall into three classes:
(Note: It is not particularly efficient to call
first to calculate the dimension of H^2(G,M), which must of course be known
if the second parameter is to be given; it is preferable to call
NonsplitExtension immediately without the second parameter (which will
return one nonsplit extension), and then to call
which will at that stage return the required dimension immediately -
all subsequent calls of
NonsplitExtension on chr will also yield
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