Coprime automorphism group

From Groupprops
Revision as of 15:57, 22 January 2009 by Vipul (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

Definition

Let G be a finite group. A subgroup H of the automorphism group \operatorname{Aut}(G) is termed a coprime automorphism group of G if the orders of G and H are relatively prime.

Note that the whole group \operatorname{Aut}(G) is very rarely coprime to G in order. Further information: Coprime automorphism group implies cyclic with order a cyclicity-forcing number