A subgroup X of a group G is called transitively normal if X is normal in any subgroup Y of G such that X≤ Y and X is subnormal in Y. Thus all subgroups of a group G are transitively normal if and only if normality is a transitive relation in every subgroup of G (i.e. G is a T¯ -group). It is proved that a group G with no infinite simple sections satisfies the minimal condition on subgroups that are not transitively normal if and only if either G is Černikov or a T¯ -group.
Groups satisfying the minimal condition on subgroups which are not transitively normal / de Giovanni, F.; Kurdachenko, L. A.; Russo, A.. - In: RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO. - ISSN 0009-725X. - 71:1(2022), pp. 397-405. [10.1007/s12215-021-00602-0]
Groups satisfying the minimal condition on subgroups which are not transitively normal
de Giovanni F.
;
2022
Abstract
A subgroup X of a group G is called transitively normal if X is normal in any subgroup Y of G such that X≤ Y and X is subnormal in Y. Thus all subgroups of a group G are transitively normal if and only if normality is a transitive relation in every subgroup of G (i.e. G is a T¯ -group). It is proved that a group G with no infinite simple sections satisfies the minimal condition on subgroups that are not transitively normal if and only if either G is Černikov or a T¯ -group.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
