Abstract
We prove the following results: (1) Every group is a maximal subgroup of some free idempotent generated semigroup. (2) Every finitely presented group is a maximal subgroup of some free idempotent generated semigroup arising from a finite semigroup. (3) Every group is a maximal subgroup of some free regular idempotent generated semigroup. (4) Every finite group is a maximal subgroup of some free regular idempotent generated semigroup arising from a finite regular semigroup. As a technical prerequisite for these results we establish a general presentation for the maximal subgroups based on a Reidemeister-Schreier type rewriting.
| Original language | English |
|---|---|
| Pages (from-to) | 147-176 |
| Number of pages | 30 |
| Journal | Israel Journal of Mathematics |
| Volume | 189 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2012 |