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.References
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Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 65 (1977), 209-214
- MSC: Primary 16A76
- DOI: https://doi.org/10.1090/S0002-9939-1977-0447351-X
- MathSciNet review: 0447351