More on groups in which each element commutes with its endomorphic images

Malone, J. J.

doi:10.1090/S0002-9939-1977-0447351-X

More on groups in which each element commutes with its endomorphic images
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by J. J. Malone PDF

Proc. Amer. Math. Soc. 65 (1977), 209-214 Request permission

Abstract:

R. Faudree has given examples of nonabelian groups which have the property cited in the title. His groups are p-groups such that (i) $Z(G) = G’ = {G^p} = U(G)$, (ii) each endomorphism $\phi$ (which is not an automorphism) has $(G)\phi \leqslant Z(G)$, and (iii) each automorphism is central. In this paper the necessity of these conditions is explored. It is also shown that, for p = 2, Faudree’s example does not in fact have the property cited in the title.

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A contribution to the theory of groups of prime power order

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