A group G is metahamiltonian if all its non-abelian subgroups are normal. It is proved here that a finitely generated soluble group is metahamiltonian if and only if all its finite homomorphic images are metahamiltonian; the behaviour of soluble minimax groups with metahamiltonian finite homomorphic images is also investigated. Moreover, groups satisfying the minimal condition on non-metahamiltonian subgroups are described.

Groups whose finite homomorphic images are metahamiltonian / DE FALCO, Maria; DE GIOVANNI, Francesco; Musella, Carmela. - In: COMMUNICATIONS IN ALGEBRA. - ISSN 0092-7872. - STAMPA. - (2009), pp. 2468-2476.

Groups whose finite homomorphic images are metahamiltonian

DE FALCO, MARIA;DE GIOVANNI, FRANCESCO;MUSELLA, CARMELA
2009

Abstract

A group G is metahamiltonian if all its non-abelian subgroups are normal. It is proved here that a finitely generated soluble group is metahamiltonian if and only if all its finite homomorphic images are metahamiltonian; the behaviour of soluble minimax groups with metahamiltonian finite homomorphic images is also investigated. Moreover, groups satisfying the minimal condition on non-metahamiltonian subgroups are described.
2009
Groups whose finite homomorphic images are metahamiltonian / DE FALCO, Maria; DE GIOVANNI, Francesco; Musella, Carmela. - In: COMMUNICATIONS IN ALGEBRA. - ISSN 0092-7872. - STAMPA. - (2009), pp. 2468-2476.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/315324
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