Balanced and functionally balanced P-groups

Abstract

In relation to Itzkowitz’s problem [5], we show that a c-bounded P-group is balanced if and only if it is functionally balanced.We prove that for an arbitrary P-group, being functionally balanced is equivalent to being strongly functionally balanced. A special focus is given to the uniform free topological group defined over a uniform P-space. In particular, we show that this group is (functionally) balanced precisely when its subsets Bn, consisting of words of length at most n, are all (resp., functionally) balanced.

Keywords

• itzkowitz’s problem
• p-group
• balanced group
• (strongly) functionally balanced group
• 54e15
• 22a05