every principal factor of a finite soluble group is elementary abelian.

Question

I am a little confused in a lot of definitions and I stuck in this exercise,this is so great if you just give me hints that I could be in right way,I really appreciate,thank you.

by principal factor, you mean $G/M$ where $M$ is maximal ? – mesel May 23 '14 at 19:47 — mesel, May 23 '14 at 19:47

Nicky Hekster · Accepted Answer · 2014-05-23T19:58:31.493

2

I assume that principal$\equiv$chief? Are you familiar with the fact that the chief factors are always characteristically simple, that is, they have no non-identity proper characteristic subgroups? In particular, a chief factor is a direct product of isomorphic simple groups. And in case of solvable groups this boils down to a direct product of cyclic groups of the same prime $p$.

edited May 23 '14 at 19:58

answered May 23 '14 at 19:47

Nicky Hekster

49,281

every principal factor of a finite soluble group is elementary abelian.

1 Answers1