On B(4, 13) 2-Groups

Abstract

A group G is said to be a B(n, k) group if for any n-element subset {a ₁,…, a _n } of G, |{a _i a _j  | 1 ≤ i, j ≤ n}| ≤k. In this article, we give a complete characterization of B(4, 13) 2-groups, and then obtain a complete characterization of B(4, 13) groups.

Key Words:

• B(n, k) Groups
• Small squaring property

2000 Mathematics Subject Classification:

• Primary: 20D60
• Secondary: 20E34

ACKNOWLEDGEMENT

This research was supported in part by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada. We would like to thank the referee for several useful suggestions.

Notes

Communicated by J.-T. Yu.