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Normal cryptogroups with an associate subgroup

Mario Petrich (2013)

Czechoslovak Mathematical Journal

Let S be a semigroup. For a , x S such that a = a x a , we say that x is an associate of a . A subgroup G of S which contains exactly one associate of each element of S is called an associate subgroup of S . It induces a unary operation in an obvious way, and we speak of a unary semigroup satisfying three simple axioms. A normal cryptogroup S is a completely regular semigroup whose -relation is a congruence and S / is a normal band. Using the representation of S as a strong semilattice of Rees matrix semigroups,...

Normal Subgroup of Product of Groups

Hiroyuki Okazaki, Kenichi Arai, Yasunari Shidama (2011)

Formalized Mathematics

In [6] it was formalized that the direct product of a family of groups gives a new group. In this article, we formalize that for all j ∈ I, the group G = Πi∈IGi has a normal subgroup isomorphic to Gj. Moreover, we show some relations between a family of groups and its direct product.

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