KNITTED SEMILATTIC STRUCTURE OF REGULAR ${\cal H}^\dag$-CYBER GROUPS

Abstract

We consider regular [Formula: see text]-cyber groups in the class of [Formula: see text]-abundant semigroups. By using knitted semilattice of semigroups, we give some structure theorems for regular [Formula: see text]-cyber groups, right quasi-normal [Formula: see text]-cyber groups and normal [Formula: see text]-cyber groups. Our main result generalizes a classical theorem of Petrich- Reilly on normal cryptic groups from the class of regular semigroups to the class of generalized abundant semigroups and also entriches a recent result of Guo-Shum on left cyber groups.