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On finite groups whose 2-Sylow subgroups have cyclic subgroups of index 2*

Published online by Cambridge University Press:  09 April 2009

W. J. Wong
W. J. Wong
Affiliation:
University of Otago.
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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.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 4 , Issue 1 , February 1964 , pp. 90 - 112
Copyright
Copyright © Australian Mathematical Society 1964

References

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