Maximal subgroups of free idempotent generated semigroups over the full transformation monoid

Details Maximal subgroups of free idempotent generated semigroups over the full transformation monoid Maximal subgroups of free idempotent generated semigroups over the full transformation monoid

2011-01-10

arxiv.org/abs/1101.1833v1

Mathematics

Group Theory

28 pages

Scientific paper

Let T_n be the full transformation semigroup of all mappings from the set
{1,...,n} to itself under composition. Let E = E(T_n) denote the set of
idempotents of T_n and let e be an arbitrary idempotent satisfying |im(e)|=r <
n-1. We prove that the maximal subgroup of the free idempotent generated
semigroup over E containing e is isomorphic to the symmetric group S_r.

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