Class-preserving implies linearly extensible

From Groupprops
Revision as of 20:25, 9 August 2008 by Vipul (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search
This article gives the statement and possibly, proof, of an implication relation between two automorphism properties. That is, it states that every automorphism satisfying the first automorphism property (i.e., class-preserving automorphism) must also satisfy the second automorphism property (i.e., linearly extensible automorphism)
View all automorphism property implications | View all automorphism property non-implications
Get more facts about class-preserving automorphism|Get more facts about linearly extensible automorphism


Let G be a group, and k a class-determining field for it. Then, any class-preserving automorphism of G is linearly extensible.


The proof combines two facts: