Constructing an Automorphism From an Anti-Automorphism
Canadian mathematical bulletin, Tome 11 (1968) no. 3, pp. 367-370
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We consider the following problem: Let G be a group with distinct automorphisms β and σ and an anti-automorphism α such that What can be said about G?If σ = α, σ is both an automorphism and an anti-automorphism so that G is abelian. Hence we assume that σ ≠ α. In this case, we show that G is non-abelian, but has an abelian subgroup of index 2. Conversely, for such a group G there always exist distinct automorphisms β and σ and an anti-automorphism α such that (1) holds.
Ayoub, Christine. Constructing an Automorphism From an Anti-Automorphism. Canadian mathematical bulletin, Tome 11 (1968) no. 3, pp. 367-370. doi: 10.4153/CMB-1968-040-6
@article{10_4153_CMB_1968_040_6,
author = {Ayoub, Christine},
title = {Constructing an {Automorphism} {From} an {Anti-Automorphism}},
journal = {Canadian mathematical bulletin},
pages = {367--370},
year = {1968},
volume = {11},
number = {3},
doi = {10.4153/CMB-1968-040-6},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1968-040-6/}
}
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