On finite groups whose 2-Sylow subgroups have cyclic subgroups of index 2
- 1 February 1964
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society
- Vol. 4 (1) , 90-112
- https://doi.org/10.1017/s1446788700022771
Abstract
If the finite group G has a 2-Sylow subgroup S of order 2a+1, containing a cyclic subgroup of index 2, then in general S may be one of the following six types [8]:(i) cyclic; (ii) Abelian of type (a, 1), a > 1; (iii) dihedral1; (iv) generalized quaternion; (v) {α, β}, α2a = β2, α2a−1+1, a ≧ 3;(vi) {α, β}, α2a = β2, α2a−1+1, a ≧ 3.Keywords
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