Every group is a maximal subgroup of the free idempotent generated semigroup over a band

Abstract

Given an arbitrary group $G$ we construct a semigroup of idempotents (band) $B_G$ with the property that the free idempotent generated semigroup over $B_G$ has a maximal subgroup isomorphic to $G$. If $G$ is finitely presented then $B_G$ is finite. This answers several questions from recent papers in the area.

8 pages, 3 figures; accepted by International Journal of Algebra and Computation (IJAC)

References in corpus (3)

• Maximal subgroups of free idempotent generated semigroups over the full linear monoid
• Subgroups of free idempotent generated semigroups need not be free
• Every group is the maximal subgroup of a naturally occurring free idempotent generated semigroup

Cited by in corpus (8)

• Free idempotent generated semigroups and endomorphism monoids of free $G$-acts
• On regularity and the word problem for free idempotent generated semigroups
• On the question of embedding a semigroup into an idempotent generated one
• Free idempotent generated semigroups over bands
• Presentations for singular wreath products
• A group-theoretical interpretation of the word problem for free idempotent generated semigroups
• Polynomial time multiplication and normal forms in free bands
• The mathematical work of K.S.S. Nambooripad