Normal subgroups as ideals. (English) Zbl 0554.20005

Šmarda, B.; Niemenmaa, M.

Arch. Math., Brno 19, 109-111 (1983).

In the paper there is studied the structure of a group G (called a K- group) with normal subgroups as ideals and the commutator operation * as the ideal operation (in the meaning of K. Aubert). The main results: 1. A group G is a K-group iff \((x*y)*y=1\) for all x,y\(\in G\). 2. Let G be a group such that G has no elements of order three. Then G is a K-group iff * is associative.

MSC:

20F12	Commutator calculus
20M12	Ideal theory for semigroups

Keywords:

normal subgroups; ideals; commutator operation