By a derived subgroup in a group G is meant the derived (or commutator) subgroup of a subgroup of G. It is natural to enquire how important the derived subgroups are within the lattice of all subgroups. Recently there has been interest in imposing restrictions on the number of derived subgroups in a group and investigating the resulting effect on the structure of the group. In this paper groups which have at most n isomorphism classes of derived subgroups (D_n-groups) are studied. A complete classification of locally finite D_3-groups into nine types is obtained. The research that led to the present paper was partially supported by a grant of the group GNSAGA of INdAM.
Locally finite groups with finitely many isomorphism classes of derived subgroups
LONGOBARDI, Patrizia;MAJ, Mercede;
2013-01-01
Abstract
By a derived subgroup in a group G is meant the derived (or commutator) subgroup of a subgroup of G. It is natural to enquire how important the derived subgroups are within the lattice of all subgroups. Recently there has been interest in imposing restrictions on the number of derived subgroups in a group and investigating the resulting effect on the structure of the group. In this paper groups which have at most n isomorphism classes of derived subgroups (D_n-groups) are studied. A complete classification of locally finite D_3-groups into nine types is obtained. The research that led to the present paper was partially supported by a grant of the group GNSAGA of INdAM.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
