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

Igor Dolinka; Nik Ruškuc

doi:10.1142/S0218196713500100

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

Group Theory 2014-03-10 v2

Authors: Igor Dolinka , Nik Ruškuc

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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.

Keywords

free idempotent generated semigroup band maximal subgroup finitely presented group semigroup theory

Cite

@article{arxiv.1301.1225,
  title  = {Every group is a maximal subgroup of the free idempotent generated semigroup over a band},
  author = {Igor Dolinka and Nik Ruškuc},
  journal= {arXiv preprint arXiv:1301.1225},
  year   = {2014}
}

Comments

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

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