Embeddings of generalized Latin squares in finite groups

Let n be a positive integer. A generalized Latin square of order n is an matrix such that the elements in each row and each column are distinct. The square is said to be commutative if the matrix is symmetric. Given , we show that for any , there exists a commutative generalized Latin square of orde...

Full description

Saved in:
Bibliographic Details
Main Authors: Chen, H.V., Chin, A.Y.M.
Format: Article
Published: 2015
Subjects:
Online Access:http://eprints.um.edu.my/16531/
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Let n be a positive integer. A generalized Latin square of order n is an matrix such that the elements in each row and each column are distinct. The square is said to be commutative if the matrix is symmetric. Given , we show that for any , there exists a commutative generalized Latin square of order n with m distinct elements which is embeddable in a finite group. We also show that for and for any where , there exists a non-commutative generalized Latin square of order n with m distinct elements which is embeddable in a finite group.