Conjugate p-Subgroups of Finite Groups
Canadian journal of mathematics, Tome 24 (1972) no. 1, pp. 17-28
Voir la notice de l'article provenant de la source Cambridge University Press
Throughout this paper, let p be a prime, P be a p-group of order pt , and φ be an isomorphism of a subgroup R of P of index p onto a subgroup Q which fixes no non-identity subgroup of P, setwise. In [2, Lemma 2.2], Glauberman shows that P can be embedded in a finite group G such that φ is effected by conjugation by some element g of G. We assume that P is thus embedded. Then Q = P ∩ Pg. Let H = 〈P,Pg〉 and V = [H,Z(Q)], so Q ⊲ H and V ⊲ H.Let E(p) be the non-abelian group of order p3 which is generated by two elements of order p. Then E(p) is dihedral if p = 2 and has exponent p if p is odd. If p is odd, then E* (p) is defined in § 2 to be a particular group of order p6 and nilpotence class three.
Currano, John J. Conjugate p-Subgroups of Finite Groups. Canadian journal of mathematics, Tome 24 (1972) no. 1, pp. 17-28. doi: 10.4153/CJM-1972-003-x
@article{10_4153_CJM_1972_003_x,
author = {Currano, John J.},
title = {Conjugate {p-Subgroups} of {Finite} {Groups}},
journal = {Canadian journal of mathematics},
pages = {17--28},
year = {1972},
volume = {24},
number = {1},
doi = {10.4153/CJM-1972-003-x},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1972-003-x/}
}
[1] 1. Currano, J., Finite p-groups with isomorphic subgroups (to appear). Google Scholar
[2] 2. Glauberman, G., Isomorphic subgroups of p-groups. I, Can. J. Math. 23 (1971), 983–1022. Google Scholar
[3] 3. Gorenstein, D., Finite groups (Harper and Row, New York, 1968). Google Scholar
[4] 4. Kurosh, A. G., The theory of groups, second English edition, translated by Hirsh, K. A. (Chelsea, New York, 1960). Google Scholar
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