On a semigroup theoretic generalization of the Kaluznin Krasner Theorem and normal extensions of inverse semigroups.
A group in a variety is said to be absolutely-, and we write , if central extensions by are again in . Absolutely-abelian groups have been classified by F. R. Beyl. In this paper we concentrate upon the class of absolutely-nilpotent of class groups. We prove some closure properties of the class and we show that every nilpotent of class group can be embedded in an -gvoup. We describe all metacyclic -groups and we characterize -generator and infinite -generator -groups. Finally...
Un sottogruppo di un gruppo si dice «almost normal» se ha soltanto un numero finito di coniugati in , e ovviamente l'insieme costituito dai sottogruppi almost normal di è un sottoreticolo del reticolo di tutti i sottogruppi di . In questo articolo vengono studiati gli isomorfismi tra reticoli di sottogruppi almost normal, provando in particolare che se è un gruppo supersolubile e è un gruppo FC-risolubile tale che i reticoli e sono isomorfi, allora anche è supersolubile, e...
We revisit the problem of deciding whether a finitely generated subgroup is a free factor of a given free group . Known algorithms solve this problem in time polynomial in the sum of the lengths of the generators of and exponential in the rank of . We show that the latter dependency can be made exponential in the rank difference rank - rank, which often makes a significant change.
We revisit the problem of deciding whether a finitely generated subgroup H is a free factor of a given free group F. Known algorithms solve this problem in time polynomial in the sum of the lengths of the generators of H and exponential in the rank of F. We show that the latter dependency can be made exponential in the rank difference rank(F) - rank(H), which often makes a significant change.
The group of all automorphisms leaving invariant every subnormal subgroup of the group is studied. In particular it is proved that is metabelian if is soluble, and that is either finite or abelian if is polycyclic.