Finite groups are big as semigroups
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We prove that a finite group G occurs as a maximal proper subsemigroup of an infinite semigroup (in the terminology of Freese, Ježek, and Nation, G is a big semigroup) if and only if |G| ≥ 3. In fact, any finite semigroup whose minimal ideal contains a subgroup with at least three elements is big.
Mathematics Subject Classification (2010)Primary 20M10 Secondary 20F05 20F50
KeywordsFinite maximal subsemigroup Rees matrix semigroup
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