G. Bergman

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dimension inequalities 1 order theory 1 poset dimension 1 poset relations 1 product posets 1

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math.GR2026

An observation on factorizations of finite groups

George M. Bergman

Given a finite group $G$ and a factorization of its order, $∣ G ∣ = a_{1} a_{2},$ we show that a sufficient condition for there to exist subsets $A_{1}, A_{2} \subseteq G$ such that $|A_1| =…

math.GR2026

Criteria for existence of semigroup homomorphisms and projective rank functions

George M. Bergman

Let $P,$ $S,$ and $T$ be semigroups, $f : P \to S$ and $g : P \to T$ semigroup homomorphisms, and $X$ a generating set for $S$ (possibly infinite). Clearly, a <i>necessary</i> condition…

math.GR2025

Adjoining universal inverses to families of elements of free monoids

George M. Bergman

Let $< X >$ be the free monoid on a generating set $X$ , and suppose one adjoins to $< X >$ universal 2-sided inverses to a finite set $S$ of its elements. We note an elementary algorit…