1,720,992 research outputs found
On groups whose subgroups are either modular or contranormal
No full texthttp://dx.doi.org/10.1017/S000497271200033
Groups with the weak minimal condition on non-normal non-abelian subgroups
No full textA group is called metahamiltonian if all its non-abelian subgroups are normal. It is proved here that a (generalized) soluble group satisfying the weak minimal condition on non-normal non-abelian subgroups is either minimax or metahamiltonian
Groups with many modular or self-normalizing subgroups
No full textIn this paper, locally graded group satisfying the minimal condition on subgroups which are neither modular nor self-normalizing are described; locally (soluble-by-finite) groups of infinite rank in which every subgroup is either modular or self-normalizing are also characterized in terms of their subgroups of infinite rank. Moreover, the results obtained are used to study groups satisfying similar restrictions on subgroups which are neither permutable nor self-normalizing
Groups with all subgroups either modular or soluble of finite rank
No full textWe study locally graded groups whose non-modular subgroups are soluble and satisfy some rank condition. In particular, in order to characterize locally graded groups whose subgroups are either modular or polycyclic, we describe (generalized) soluble groups whose non-modular subgroups are finitely generated
Groups with restricted non-permutable subgroups
No full textA subgroup H of a group G is said to be permutable if HK = KH for every subgroup K of G and the group G is called metaquasihamiltonian if all subgroups of G are either permutable or abelian. It is known that a locally graded metaquasihamiltonian group G is soluble with derived length at most 4 and contains a finite normal subgroup N such that all subgroups of the factor G/N are permutable. In this paper, we describe locally graded groups in which the set of all nonmetaquasihamiltonian subgroups satisfies the minimal condition and locally graded groups with the minimal condition on subgroups which are neither abelian nor permutable. Moreover, it is proved here that a finitely generated hyper-(abelian or finite) group whose finite homomorphic images are metaquasihamiltonian is itself metaquasihamiltonian
On groups with all proper subgroups finite-by-abelian-by-finite
No full textWe show that if all proper subgroups of a locally graded group G are finite-by-abelian-by-finite, then G contains a finite normal subgroup N such that all proper subgroups of G/N are abelian-by-finite. Then we apply this result to the study of groups which are minimal-non-P also for related group properties P. Finally we see how for locally (soluble-by-finite) groups of infinite rank, it is enough to restrict attention to the proper subgroups with infinite rank
GROUPS WITH THE REAL CHAIN CONDITION ON NON-PRONORMAL SUBGROUPS
No full textIt is shown that a generalised radical group has no chain of non-pronormal subgroups with the same order type as the set R of the real numbers if and only if either the group is minimax or all subgroups are pronormal
Groups in which each subnormal subgroup is commensurable with some normal subgroup
No full textWe study groups in which each subnormal subgroup is commensurable with a normal subgroup. Recall that two subgroups and are termed commensurable if H-KHcap K has finite index in both and . Among other results, we show that if a (sub)soluble group has the above property, then is finite-by-metabelian, i.e., GG{} is finite
- …
