Cyclic Groups and Primitive Roots

1995 ◽  
pp. 353-362
Author(s):  
Lindsay N. Childs
Keyword(s):  
Cyclic Groups ◽  
Primitive Roots

scholarly journals The average time complexity of probabilistic algorithms for finding generators in finite cyclic groups

2015 ◽  
Vol 63 (4) ◽  
pp. 989-996
Author(s):  
T. Adamski ◽  
W. Nowakowski
Keyword(s):  
Time Complexity ◽  
Secure Communication ◽  
Key Agreement ◽  
Probabilistic Algorithms ◽  
Cyclic Groups ◽  
Secure Information ◽  
Cryptographic Algorithms ◽  
Entity Identification ◽  
Primitive Roots ◽  
Electronic Administration

Abstract Generators of finite cyclic groups play important role in many cryptographic algorithms like public key ciphers, digital signatures, entity identification and key agreement algorithms. The above kinds of cryptographic algorithms are crucial for all secure communication in computer networks and secure information processing (in particular in mobile services, banking and electronic administration). In the paper, proofs of correctness of two probabilistic algorithms (for finding generators of finite cyclic groups and primitive roots) are given along with assessment of their average time computational complexity.

On the minimal varieties of PI-algebras graded by finite cyclic groups

2021 ◽  
pp. 1-25
Author(s):  
Marcos Antônio da Silva Pinto ◽  
Viviane Ribeiro Tomaz da Silva
Keyword(s):  
Cyclic Groups

scholarly journals Serre’s Property (FA) for automorphism groups of free products

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Naomi Andrew
Keyword(s):  
Automorphism Group ◽  
Free Product ◽  
Finite Groups ◽  
Automorphism Groups ◽  
Sufficient Conditions ◽  
Free Products ◽  
Cyclic Groups ◽  
Link Type ◽  
Open Case

AbstractWe provide some necessary and some sufficient conditions for the automorphism group of a free product of (freely indecomposable, not infinite cyclic) groups to have Property (FA). The additional sufficient conditions are all met by finite groups, and so this case is fully characterised. Therefore, this paper generalises the work of N. Leder [Serre’s Property FA for automorphism groups of free products, preprint (2018), https://arxiv.org/abs/1810.06287v1]. for finite cyclic groups, as well as resolving the open case of that paper.

scholarly journals Cubulating hyperbolic free-by-cyclic groups: The irreducible case

2016 ◽  
Vol 165 (9) ◽  
pp. 1753-1813 ◽  
Author(s):  
Mark F. Hagen ◽  
Daniel T. Wise
Keyword(s):  
Cyclic Groups

scholarly journals The Segal Conjecture for Cyclic Groups

1981 ◽  
Vol 13 (1) ◽  
pp. 42-44 ◽  
Author(s):  
Douglas C. Ravenel
Keyword(s):  
Cyclic Groups

scholarly journals On connectedness of power graphs of finite groups

2018 ◽  
Vol 17 (10) ◽  
pp. 1850184 ◽  
Author(s):  
Ramesh Prasad Panda ◽  
K. V. Krishna
Keyword(s):  
Finite Groups ◽  
Upper Bound ◽  
The Other ◽  
Number Of Components ◽  
Cyclic Groups ◽  
Power Graph ◽  
Vertex Set ◽  
Proper Power

The power graph of a group [Formula: see text] is the graph whose vertex set is [Formula: see text] and two distinct vertices are adjacent if one is a power of the other. This paper investigates the minimal separating sets of power graphs of finite groups. For power graphs of finite cyclic groups, certain minimal separating sets are obtained. Consequently, a sharp upper bound for their connectivity is supplied. Further, the components of proper power graphs of [Formula: see text]-groups are studied. In particular, the number of components of that of abelian [Formula: see text]-groups are determined.

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