共查询到20条相似文献,搜索用时 21 毫秒
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Let ? be a class of groups and G a finite group. We call a set Σ of subgroups of G a G-covering subgroup system for ? if G ∈ ? whenever Σ ? ?. For a non-identity subgroup H of G, we put Σ H be some set of subgroups of G which contains at least one supplement in G of each maximal subgroup of H. Let p ≠ q be primes dividing |G|, P, and Q be non-identity a p-subgroup and a q-subgroup of G, respectively. We prove that Σ P and Σ P ∪ Σ Q are G-covering subgroup systems for many classes of finite groups. 相似文献
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Takashi Okuyama 《代数通讯》2013,41(4):1155-1165
Let G be an arbitrary Abelian group. A subgroup A of G is said to be quasi-purifiable in G if there exists a pure subgroup H of G containing A such that A is almost-dense in H and H/A is torsion. Such a subgroup H is called a “quasi-pure hull” of A in G. We prove that if G is an Abelian group whose maximal torsion subgroup is torsion-complete, then all subgroups A are quasi-purifiable in G and all maximal quasi-pure hulls of A are isomorphic. Every subgroup A of a torsion-complete p-primary group G is contained in a minimal direct summand of G that is a minimal pure torsion-complete subgroup containing A. An Abelian group G is said to be an “ADE decomposable group” if there exist an ADE subgroup K of G and a subgroup T′ of T(G) such that G = K⊕ T′. An Abelian group whose maximal torsion subgroup is torsion-complete is ADE decomposable. Hence direct products of cyclic groups are ADE decomposable groups. 相似文献
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Fatemeh Vosooghpour 《代数通讯》2013,41(4):1292-1299
Let G be a group. If the set 𝒜(G) = {α ∈Aut(G) | xα(x) = α(x)x, for all x ∈ G} forms a subgroup of Aut(G), then G is called 𝒜(G)-group. We show that the minimum order of a non-𝒜(G) p-group is p 5 for any prime p. We also find the smallest group order of a non-𝒜(G) group. This is related to a question introduced by Deaconescu, Silberberg, and Walls [4]. Moreover, we prove that for any prime p and for all integer n ≥ 5, there exists a non-𝒜(G) group of order p n . 相似文献
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We classify finite p-groups all of whose nonnormal subgroups have orders at most p3, p odd prime. Together with a known result, we completely solved Problem 2279 proposed by Y. Berkovich and Z. Janko in Groups of Prime Power Order, Vol. 3. 相似文献
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《代数通讯》2013,41(7):3497-3504
Abstract In this paper,we present a sharp bound for the nilpotency class of a finite p-group (where p is an odd prime) in terms of its coexponent. As to a powerful p-group,we give the sharp bound for the nilpotency class in terms of its coexponent for arbitrary prime p. 相似文献
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ZHANG JunQiang & LI XianHua School of Mathematical Sciences Soochow University Suzhou China 《中国科学 数学(英文版)》2010,(5)
Let G be a finite p-group.If the order of the derived subgroup of each proper subgroup of G divides pi,G is called a Di-group.In this paper,we give a characterization of all D1-groups.This is an answer to a question introduced by Berkovich. 相似文献
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A. Abdollahi 《代数通讯》2017,45(8):3636-3642
A longstanding conjecture asserts that every finite nonabelian p-group admits a noninner automorphism of order p. In this paper we give some necessary conditions for a possible counterexample G to this conjecture, in the case when G is a 2-generator finite p-group. Then we show that every 2-generator finite p-group with abelian Frattini subgroup has a noninner automorphism of order p. 相似文献
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Manoj K. Yadav 《代数通讯》2013,41(12):4325-4331
Let G be a finite p-group of nilpotency class 2. We find necessary and sufficient conditions on G such that each central automorphism of G fixes the center of G element-wise. 相似文献
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Victor S. Monakhov 《代数通讯》2020,48(1):93-100
AbstractA subgroup H of a finite group G is said to be Hall subnormally embedded in G if there is a subnormal subgroup N of G such that H is a Hall subgroup of N. A Schmidt group is a finite non-nilpotent group whose all proper subgroups are nilpotent. We prove the nilpotency of the second derived subgroup of a finite group in which each Schmidt subgroup is Hall subnormally embedded. 相似文献
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Mohamed Asaad 《代数通讯》2013,41(6):2319-2330
Let G be a finite group. A subgroup H of G is said to be weakly s-supplemented in G if there exists a subgroup K of G such that G = HK and H ∩ K ≤ H s G , where H s G is the subgroup of H generated by all those subgroups of H which are s-quasinormal in G. In this article, we investigate the structure of G under the assumption that some families of subgroups of G are weakly s-supplemented in G. Some recent results are generalized. 相似文献
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Victor S. Monakhov 《代数通讯》2020,48(2):668-675
AbstractA subgroup H of a finite group G is said to be Hall subnormally embedded in G if there is a subnormal subgroup N of G such that H is a Hall subgroup of N. A Schmidt group is a finite non-nilpotent group whose all proper subgroups are nilpotent. We prove the nilpotency of the second derived subgroup of a finite group in which each Schmidt subgroup is Hall subnormally embedded. 相似文献
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Summary A subgroup H of a group G is said to be π-quasinormal in G if it permutes with every Sylow subgroup of G, and H is said to be π-quasinormally embedded in G if for each prime dividing the order of H, a Sylow p-subgroup of H is also a Sylow p-subgroup of some π-quasinormal subgroups of G. We characterize p-nilpotentcy of finite groups with the assumption that some maximal subgroups, 2-maximal subgroups, minimal subgroups and 2-minimal subgroups are π-quasinormally embedded, respectively. 相似文献
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We define a particular type of automorphisms called transvections on a finite finite abelian p-group Hp. It is proved that the subgroup E of the automorphism group Aut(Hp) of Hp generated by those transvections is normal in it, and that Aut(Hp) can be written as the product of E and some abelian subgroup K. The center of Aut(Hp) is also determined. 相似文献