[Next][Prev] [Right] [Left] [Up] [Index] [Root]

Miscellanous p-group functions

NumberOfSubgroupsAbelianPGroup (A) : SeqEnum -> SeqEnum
Return the number of subgroups of each non-trivial order in the abelian p-group G where A = [a_1, a_2, ... ] and G = C_(a_1) x C_(a_2) x ... . The m-th entry in the sequence returned is the number of subgroups of order p^m.
OrderAutomorphismGroupAbelianPGroup (A) : SeqEnum -> RngIntElt
Order of automorphism group of abelian p-group G where A = [a_1, a_2, ... ] and G = C_(a_1) x C_(a_2) x ... .

Example GrpPGp_subgroupsabelianpgroups (H20E7)

Subgroups of C_4 x C_8 x C_(64).

> NumberOfSubgroupsAbelianPGroup ([4, 8, 64]);
[ 7, 35, 91, 139, 171, 171, 139, 91, 35, 7, 1 ]
Hence, for example, there are 7 subgroups of order 2 and 139 subgroups of order 2^4.

> OrderAutomorphismGroupAbelianPGroup ([4, 8, 64]);
4194304

 [Next][Prev] [Right] [Left] [Up] [Index] [Root]