Sequences with group products from finite regular semigroups (Q1874359)

A formula for the number \(g_r(n)\) is found which is the smallest integer such that for each regular semigroup \(S\) of order \(n\), each sequence of length \(g_r(n)\) of elements of \(S\) contains a segment the product of whose elements is a group element of \(S\). This extends results of a similar kind obtained by the same author [ibid. 220, No. 1-3, 159-170 (2000; Zbl 0953.20047)] as well as \textit{T. E. Hall} and \textit{M. V. Sapir} [ibid. 161, No. 1-3, 151-160 (1996; Zbl 0871.20051)].