# On NR*-subgroups of finite groups

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In 1973, I. N. AbramovskiÄ initiated the study of groups in which the transitivity condition is imposed on abelian normal subgroups only. He studied these locally finite groups under the additional restriction of commutativity of their Sylow p-subgroups. Much later the groups in which all...

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Let â„± be a class of groups and let G be a finite group. We call a set Î£ of subgroups of G a covering subgroup system of G for â„± (or directly an â„±-covering subgroup system of G) if G âˆˆ â„± whenever every subgroup in Î£ is in â„±. We give some covering subgroup...

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In this paper, the following concept is introduced: A subgroup H of G is said to be X-ss-permutable in G if there is a nonempty subset X of G and H is X-permutable with all Sylow subgroups of some supplement T of H to G. In this paper, groups with certain X-ss-permutable subgroups of prime power...