Abstract. Let FC0 be the class of all finite groups, and for each non-negative integer m define by induction the group class FCm+1 consisting of all groups G such that the factor group G/CG(xG) has the property FCm for all elements x of G. Clearly, FC1 is the class of FC-groups and every nilpotent group with class at most m belongs to FCm. The class of FCm-groups was introduced in [6]. In this article the structure of groups with finitely many normalizers of non-FCm-subgroups (respectively, the structure of groups whose subgroups either are subnormal with bounded defect or have the property FCm) is investigated.
Groups with many generalized FC-subgroups
VINCENZI, Giovanni;
2009
Abstract
Abstract. Let FC0 be the class of all finite groups, and for each non-negative integer m define by induction the group class FCm+1 consisting of all groups G such that the factor group G/CG(xG) has the property FCm for all elements x of G. Clearly, FC1 is the class of FC-groups and every nilpotent group with class at most m belongs to FCm. The class of FCm-groups was introduced in [6]. In this article the structure of groups with finitely many normalizers of non-FCm-subgroups (respectively, the structure of groups whose subgroups either are subnormal with bounded defect or have the property FCm) is investigated.File in questo prodotto:
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