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) , (ii) each endomorphism (which is not an automorphism) has , 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