ANALYSIS OF THE IMPLEMENTATION COMPLEXITY OF CRYPTOSYSTEM BASED ON THE SUZUKI GROUP

2019 ◽  
Vol 78 (5) ◽  
pp. 419-427 ◽  
Author(s):  
G. Z. Khalimov ◽  
E. V. Kotukh ◽  
Yu. O. Serhiychuk ◽  
O. S. Marukhnenko
Keyword(s):  
Suzuki Group

scholarly journals Broué's abelian defect group conjecture for the Held group and the sporadic Suzuki group

2004 ◽  
Vol 279 (2) ◽  
pp. 638-666 ◽  
Author(s):  
Shigeo Koshitani ◽  
Naoko Kunugi ◽  
Katsushi Waki
Keyword(s):  
Defect Group ◽  
Suzuki Group ◽  
Held Group

scholarly journals On the involution fixity of exceptional groups of Lie type

2018 ◽  
Vol 28 (03) ◽  
pp. 411-466 ◽  
Author(s):  
Timothy C. Burness ◽  
Adam R. Thomas
Keyword(s):  
Algebraic Geometry ◽  
Fixed Points ◽  
Algebraic Groups ◽  
Natural Analogue ◽  
Transitive Action ◽  
Exceptional Groups ◽  
Closed Fields ◽  
Suzuki Group ◽  
Algebraically Closed Fields ◽  
Groups Of Lie Type

The involution fixity [Formula: see text] of a permutation group [Formula: see text] of degree [Formula: see text] is the maximum number of fixed points of an involution. In this paper we study the involution fixity of primitive almost simple exceptional groups of Lie type. We show that if [Formula: see text] is the socle of such a group, then either [Formula: see text], or [Formula: see text] and [Formula: see text] is a Suzuki group in its natural [Formula: see text]-transitive action of degree [Formula: see text]. This bound is best possible and we present more detailed results for each family of exceptional groups, which allows us to determine the groups with [Formula: see text]. This extends recent work of Liebeck and Shalev, who established the bound [Formula: see text] for every almost simple primitive group of degree [Formula: see text] with socle [Formula: see text] (with a prescribed list of exceptions). Finally, by combining our results with the Lang–Weil estimates from algebraic geometry, we determine bounds on a natural analogue of involution fixity for primitive actions of exceptional algebraic groups over algebraically closed fields.

scholarly journals Recognizability of finite groups by Suzuki group

2019 ◽  
pp. 225-228
Author(s):  
Alireza Khalili Asboei ◽  
Seyed Sadegh Salehi Amiri
Keyword(s):  
Finite Groups ◽  
Suzuki Group
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