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Finite groups whose minimal subgroups are normal
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This article is published in Mathematische Zeitschrift.The article was published on 1970-03-01. It has received 202 citations till now. The article focuses on the topics: Locally finite group & Sporadic group.read more
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THE $c$-SUPPLEMENTED PROPERTY OF FINITE GROUPS
Huaquan Wei,Yanming Wang +1 more
TL;DR: In this paper, the influence of minimal subgroups on finite groups' nilpotence and supersolvability was studied and the effect of $c$-supplemented minimal subgroup on the $p$-nilpotency of finite groups was analyzed.
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On c-supplemented subgroups of finite groups
TL;DR: In this paper, the structure of a finite group under the assumption that some families of subgroups of G are c -supplemented in G is investigated, and it is shown that a subgroup H of G is said to be c -sub-sub-group in G if H G = ⋂ g ∈ G H g is the largest normal subgroup contained in H G.
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On the intersection of all maximal F-subgroups of a finite group
TL;DR: In this article, the influence of the subgroup Σ F (G ) on the structure of a finite group G was studied, where F denotes the intersection of all maximal F -subgroups of G.
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Finite Groups Whose Minimal Subgroups are c-Supplemented
Mohamed Asaad,Mohamed A. Ramadan +1 more
TL;DR: In this paper, the structure of a finite group G under the assumption that subgroups of prime order are c-supplemented in G is investigated, and it is shown that the minimal subgroup of the generalized Fitting subgroup F ∗(G) of G is the largest normal subgroup contained in G.
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On weakly τ-quasinormal subgroups of finite groups
TL;DR: In this paper, it was shown that a Sylow subgroup of a finite group is weakly τ-quasinormal if it has a subnormal subgroup T such that HT = G and T ∩ H ≦ H¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ τG¯¯¯¯, where T is the subgroup generated by all those subgroups of H which are τ-QUASINormal in G.
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Finite groups in which the nonnormal subgroups have nontrivial intersection
TL;DR: In this article, the authors give an example of such a group and obtain the non-Abelian Dedekind groups of order a power of 2 by taking -4 to be the direct product of a cyclic group of order 4 with an elementary Abelian group and ~2 to be a unique element of J which is a square.