G. Bergman

activity

20032026

most citedGenerating infinite symmetric groups

52 citations · 217 across the 45 of their papers we have counts for

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Showing 2026Show all

3 papers · 1 filter

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.CO2026

Further thoughts on dimensions of posets

George M. Bergman

We recall the concept of the dimension of a finite poset $P$ , and the longstanding conjecture that for all finite nonempty posets $P$ and $Q$ , $\dim(P\times Q)\geq\dim(P)+\dim(Q)-2…

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…