Maximal non-commuting sets in certain unipotent upper-triangular linear groups

Abstract

Abstract. We find the exact size of a maximal non-commuting set in unipotent upper triangular linear group U U4(Fq) in terms of a non-commuting geometric structure (Refer Definition 10), where Fq is the finite field with q elements. Then we get bounds on the size of such a set by explicitly finding certain non-commuting sets in the non-commuting strucuture.