Vol. 81, No. 1, 1979

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Automorphism groups retracting onto symmetric groups

Matthew Gould and Helen H. James

Vol. 81 (1979), No. 1, 93–100
Abstract

The main result of this note is that if a group G retracts onto the symmetric group Sn ( 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
Authors
Matthew Gould
Helen H. James