Semi-Homomorphisms of Groups
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 384-388
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A mapping φ from one group, G, into another, H, is said to be a semi-homomorphism of G if φ(aba) = φ(a) φ(b) φ a) for all a, b ∊G. Clearly any homomorphism or anti-homomorphism is a semi-homomorphism; the converse, however, need not be true in general. It is perfectly clear what one intends by a semi-isomorphism or semi-automorphism.Our purpose here is to show that for a rather general situation a semi-homomorphism turns out to be a homomorphism or an anti-homomorphism. In (2) we proved that any semi-automorphism of a simple group which contains an element of order 4 must automatically be either an automorphism or an anti-automorphism.
Herstein, I. N. Semi-Homomorphisms of Groups. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 384-388. doi: 10.4153/CJM-1968-034-7
@article{10_4153_CJM_1968_034_7,
author = {Herstein, I. N.},
title = {Semi-Homomorphisms of {Groups}},
journal = {Canadian journal of mathematics},
pages = {384--388},
year = {1968},
volume = {20},
number = {1},
doi = {10.4153/CJM-1968-034-7},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1968-034-7/}
}
[1] 1. Feit, Walter and Thompson, John, Solvability of groups of odd order, Pacific J. Math., 13 1963), 775–1029. Google Scholar
[2] 2. Herstein, I. N. and Ruchte, M. F., Semi-automorphisms of groups, Proc. Amer. Math. Soc, 9 (1958), 145–150. Google Scholar
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