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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13 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.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…

math.GR2020★ 4 cited

On core quandles of groups

George M. Bergman

We review the definition of a quandle, and in particular of the core quandle $Core (G)$ of a group $G$ , which consists of the underlying set of $G$ , with the binary operati…

math.GR2020

A note on factorizations of finite groups

George M. Bergman

In Question 19.35 of the Kourovka Notebook, M. H. Hooshmand asks whether, given a finite group $G$ and a factorization $card (G) = n_{1} \dots n_{k}$ , one can always find subset…

math.GR2019★ 1 cited

Which group algebras cannot be made zero by imposing a single non-monomial relation?

George M. Bergman

For which groups $G$ is it true that for all fields $k$ , every non-monomial element of the group algebra $k G$ generates a proper $2$ -sided ideal? The only groups for which we kno…