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- W2991361408 abstract "Given a group (X) we study the algebraic structure of its superextension (lambda(X)). This is a right-topological semigroup consisting of all maximal linked systems on (X) endowed with the operation (mathcal Acircmathcal B={Csubset X:{xin X:x^{-1}Cinmathcal B}inmathcal A}) that extends the group operation of (X). We characterize right zeros of (lambda(X)) as invariant maximal linked systems on (X) and prove that (lambda(X)) has a right zero if and only if each element of (X) has odd order. On the other hand, the semigroup (lambda(X)) contains a left zero if and only if it contains a zero if and only if (X) has odd order (|X|le5). The semigroup (lambda(X)) is commutative if and only if (|X|le4). We finish the paper with a complete description of the algebraic structure of the semigroups (lambda(X)) for all groups (X) of cardinality (|X|le5)." @default.
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- W2991361408 date "2008-02-01" @default.
- W2991361408 modified "2023-09-23" @default.
- W2991361408 title "Algebra in superextensions of groups, I: zeros and commutativity" @default.
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