On automorphisms of A-groups |
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Authors: | Martin R Pettet |
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Institution: | (1) Department of Mathematics, The University of Toledo, Toledo, Ohio, 43606, U.S.A |
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Abstract: | Let G be an A-group (i.e. a group in which xx
α
= x
α
x for all and let denote the subgroup of Aut(G) consisting of all automorphisms that leave invariant the centralizer of each element of G. The quotient is an elementary abelian 2-group and natural analogies exist to suggest that it might always be trivial. It is shown that,
in fact, for any odd prime p and any positive integer r, there exist infinitely many finite pA-groups G for which has rank r.
Received: 23 March 2008, Revised: 20 May 2008 |
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Keywords: | " target="_blank"> A-group graph automorphism |
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