[GAP Forum] About permutable

[Ramon Esteban-Romero]

Dear Jianjun, dear forum,

Adolfo Ballester-Bolinches and I are preparing a GAP package to check
permutability of subgroups in finite groups and to decide whether a
finite has all subnormal subgroups normal or permutable, among other
things. According to a result of Iwasawa, these groups are nilpotent
and have a Sylow p-subgroup P which satisfies one of the following two
conditions:
- P is a direct product of a quaternion group of order 8 and an
elementary abelian 2-group, or
- P has an abelian normal subgroup A and an element b such that
$P=A\langle b\rangle$ and there exists a natural number s, which is
greater than 1 if p=2, such that a^b=a^{1+p^s} for all a in A.

The package includes functions which perform this test. The package is
almost finished, we are making the final revision of the package and
the documentation. We hope to submit it soon to be refereed. We can
send you a preliminary version of the package if you want.

With best wishes,
-- 
Ramon <resteban at mat.upv.es>

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Telèfon/teléfono/téléphone/phone: (+34)963877007 ext. 76676

* 刘建军 <ljj198123 at 126.com> [110713 19:29]:
> Dear forum,
>  
> A subgroup H of a finite group G is said to be permutable if HK=KH for every subgroup K of G.
>  
> I would like to know whether all subgroups of a group G are permutable.
> Is there a method to get it in GAP?
>  
> Best Wishes
> Jianjun Liu
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