Uniform Cyclic Group Factorizations of Finite Groups

by   Kazuki Kanai, et al.
Ibaraki University

In this paper, we introduce a kind of decomposition of a finite group called a uniform group factorization, as a generalization of exact factorizations of a finite group. A group G is said to admit a uniform group factorization if there exist subgroups H_1, H_2, …, H_k such that G = H_1 H_2 ⋯ H_k and the number of ways to represent any element g ∈ G as g = h_1 h_2 ⋯ h_k (h_i ∈ H_i) does not depend on the choice of g. Moreover, a uniform group factorization consisting of cyclic subgroups is called a uniform cyclic group factorization. First, we show that any finite solvable group admits a uniform cyclic group factorization. Second, we show that whether all finite groups admit uniform cyclic group factorizations or not is equivalent to whether all finite simple groups admit uniform group factorizations or not. Lastly, we give some concrete examples of such factorizations.


page 1

page 2

page 3

page 4


Limit groups and groups acting freely on ^n-trees

We give a simple proof of the finite presentation of Sela's limit groups...

Solutions of the Multivariate Inverse Frobenius–Perron Problem

We address the inverse Frobenius–Perron problem: given a prescribed targ...

Acyclicity in finite groups and groupoids

We expound a simple construction of finite groups and groupoids whose Ca...

A topological dynamical system with two different positive sofic entropies

A sofic approximation to a countable group is a sequence of partial acti...

Voting on Cyclic Orders, Group Theory, and Ballots

A cyclic order may be thought of informally as a way to seat people arou...

Equal partners do better in defensive alliances

Cyclic dominance offers not just a way to maintain biodiversity, but als...

Notation for Subject Answer Analysis

It is believed that consistent notation helps the research community in ...

Please sign up or login with your details

Forgot password? Click here to reset