Every group is a maximal subgroup of the free idempotent generated semigroup over a band
classification
🧮 math.GR
keywords
semigroupbandfreegeneratedgroupidempotentmaximalsubgroup
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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.
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