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Proceedings of the American Mathematical Society

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


Author: J. J. Malone
Journal: Proc. Amer. Math. Soc. 65 (1977), 209-214
MSC: Primary 16A76
MathSciNet review: 0447351
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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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DOI: https://doi.org/10.1090/S0002-9939-1977-0447351-X
Keywords: Finite group, nilpotent class 2 group, endomorphic images, endomorphism near ring
Article copyright: © Copyright 1977 American Mathematical Society