Many non-embeddable infinite groups
Group Theory
2026-01-08 v7
Abstract
Let K be a set of infinite cardinals such that the cardinality of K is the first strong limit cardinal greater than uncountably many strong limit cardinals. We construct a family of pairwise non-embeddable groups which contains 2^k groups of order k for every cardinal number k in K. (In particular, in this family small groups are never embeddable in large groups.)
Cite
@article{arxiv.2401.17962,
title = {Many non-embeddable infinite groups},
author = {Gerald Kuba},
journal= {arXiv preprint arXiv:2401.17962},
year = {2026}
}