On ARX-like ciphers based on different codings of 2-groups with a cyclic subgroup of index 2

2021 ◽  
pp. 100-104
Author(s):  
B. A. Pogorelov ◽  
M. A. Pudovkina
Keyword(s):  
Cyclic Subgroup ◽  
Index 2

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.

scholarly journals An Extension Theorem for Terraces

10.37236/2161 ◽  
2013 ◽  
Vol 20 (2) ◽  
Author(s):  
Matt Ollis ◽  
Devin Willmott
Keyword(s):  
Cyclic Subgroup ◽  
Dihedral Group ◽  
Abelian Groups ◽  
Extension Theorem ◽  
Group V ◽  
Index 2

We generalise an extension theorem for terraces for abelian groups to apply to non-abelian groups with a central subgroup isomorphic to the Klein 4-group $V$.  We also give terraces for three of the non-abelian groups of order a multiple of 8 that have a cyclic subgroup of index 2 that may be used in the extension theorem.  These results imply the existence of terraces for many groups that were not previously known to be terraced, including 27 non-abelian groups of order 64 and all groups of the form $V^s \times D_{8k}$ for all $s$ and all $k > 1$ where $D_{8k}$ is the dihedral group of order $8k$.  

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