A Note on Split Extensions of Finite Groups
Canadian mathematical bulletin, Tome 24 (1981) no. 1, pp. 117-119
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Let N and K be finite groups with K acting on N, and let G be the semidirect product NK It was shown by Zassenhaus that if (|N|, |K|) — 1 and either N or K is solvable (an assumption later rendered redundant by the Feit-Thompson theorem), then all complements of N in G are conjugate to K.
Pettet, Martin R. A Note on Split Extensions of Finite Groups. Canadian mathematical bulletin, Tome 24 (1981) no. 1, pp. 117-119. doi: 10.4153/CMB-1981-020-4
@article{10_4153_CMB_1981_020_4,
author = {Pettet, Martin R.},
title = {A {Note} on {Split} {Extensions} of {Finite} {Groups}},
journal = {Canadian mathematical bulletin},
pages = {117--119},
year = {1981},
volume = {24},
number = {1},
doi = {10.4153/CMB-1981-020-4},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-020-4/}
}
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