Author
Zdravka Bozikov
Bio: Zdravka Bozikov is an academic researcher. The author has contributed to research in topics: Locally finite group. The author has an hindex of 1, co-authored 1 publications receiving 14 citations.
Topics: Locally finite group
Papers
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TL;DR: In this paper, a complete classification of finite p-groups all of whose noncyclic subgroups are normal is given, which solves a problem stated by Berkovich and solves the problem of non-cyclical subgroups.
Abstract: We give a complete classification of finite p-groups all of whose noncyclic subgroups are normal, which solves a problem stated by Berkovich.
14 citations
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TL;DR: In this article, a framework for generalisations of Baer's norm has been given for a class of finite nilpotent groups, where the C -norm κ C (G ) of a finite group G is defined as the intersection of the normalisers of the subgroups of G not in C.
16 citations
TL;DR: In this paper, it was shown that if G.G.G is a non-cyclic subgroup, then the subgroup A(G) is the intersection of the normalizers of all noncyclic groups of G.
Abstract: G, we dene the subgroup A(G) to be intersection of the normalizers of all non-cyclic subgroups of G. Set A0 = 1. Dene Ai+1(G)=Ai(G) = A(G=Ai(G)) for i 1. By A1 (G) denote the terminal term of the ascending series. It is proved that if G.
9 citations
TL;DR: In this article, the intersection of the normalizers of all non-cyclic subgroups of a finite group G is studied and the results of Passman, Bozikov, and Janko are extended to non-nilpotent finite groups.
Abstract: Baer and Wielandt in 1934 and 1958, respectively, considered that the intersection of the normalizers of all subgroups of G and the intersection of the normalizers of all subnormal subgroups of G. In this article, for a finite group G, we define the subgroup S(G) to be intersection of the normalizers of all non-cyclic subgroups of G. Groups whose noncyclic subgroups are normal are studied in this article, as well as groups in which all noncyclic subgroups are normalized by all minimal subgroups. In particular, we extend the results of Passman, Bozikov, and Janko to non-nilpotent finite groups.
7 citations
TL;DR: In this paper, it was shown that if the integral group ring Z [ G ] satisfies the multiplicative Jordan decomposition property, then every noncyclic subgroup of G is normal.
4 citations
TL;DR: In this paper, it was shown that if G is a nonabelian semidirect product of the form C p ⋊ C 3 k, with prime p > 7 and the cyclic 3-group acting like a group of order 3, then Z [ G ] does not have MJD.
4 citations