scholarly journals On a class of power piecewise affine permutations on nonabelian groups of order 2m with cyclic subgroups of index 2

2019 ◽  
pp. 27-29
Author(s):  
B. A. Pogorelov ◽  
M. A. Pudovkina
Keyword(s):  
Cyclic Subgroups ◽  
Piecewise Affine ◽  
Index 2 ◽  
Affine Permutations ◽  
Nonabelian Groups

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

1964 ◽  
Vol 4 (1) ◽  
pp. 90-112 ◽  
Author(s):  
W. J. Wong
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Sylow Subgroup ◽  
Cyclic Subgroup ◽  
Sylow Subgroups ◽  
Cyclic Subgroups ◽  
Index 2 ◽  
Generalized Quaternion

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.

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