Automorphism groups retracting onto symmetric groups

Matthew Gould and Helen H. James

Vol. 81 (1979), No. 1, 93–100

DOI: 10.2140/pjm.1979.81.93

Abstract

The main result of this note is that if a group G retracts onto the symmetric group S_n ( n finite) then G is isomorphic to the automorphism group of the n-th direct power of a multi-unary algebra (equivalently: G is isomorphic to the automorphism group of an algebra that is free on a basis of n elements). It will be shown that the converse fails for all n > 1, but a restricted form of the converse will be proved.

Mathematical Subject Classification 2000

Primary: 20F29

Milestones

Received: 21 November 1977

Published: 1 March 1979