Generalized subgroups and homomorphisms (Q5930095)

The authors define ``generalized groups'' and claim this concept was introduced by the second author in 1998. Generalized groups are precisely completely regular semigroups. They define normal generalized groups as orthogroups (that is, completely regular semigroups in which idempotents form a subsemigroup) and conjecture that every generalized group is normal. Counterexamples to this conjecture have been known for 80 years. Homomorphisms and an analog of group kernels for homomorphisms are defined. All these results are well known.