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1.
A subgroup H of a finite group G is said to be permutable in G if it permutes with every subgroup of G. In this paper, we determine the finite groups which have a permutable subgroup of prime order and whose maximal subgroups
are totally (generalized) smooth groups. 相似文献
2.
AbstractIn this paper, we introduce the concept of sse-embedded subgroups of finite groups and present some new characterizations of solubility of finite groups using the sse-embedding property of subgroups. Furthermore, we discuss the sse-embedded subgroups in finite nonabelian simple groups. Some previously known results are generalized and unified. 相似文献
3.
For a finite group G, let n(G) denote the number of conjugacy classes of non-subnormal subgroups of G. In this paper, we show that a finite group G satisfying n(G)≤2|π(G)| is solvable, and for a finite non-solvable group G, n(G) = 2|π(G)|+1 if and only if G?A5. 相似文献
4.
Selçuk Kayacan 《代数通讯》2017,45(6):2466-2477
The intersection graph of a group G is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper non-trivial subgroups of G, and there is an edge between two distinct vertices H and K if and only if H∩K≠1 where 1 denotes the trivial subgroup of G. In this paper we classify all finite groups whose intersection graphs are K3,3-free. 相似文献
5.
Y. Contreras-Rojas 《代数通讯》2017,45(8):3606-3609
By 𝔛(n) we denote the variety of all groups satisfying the law [x,y]n≡1, that is, groups with commutators of order dividing n. Let p be a prime and G a finite group whose Sylow p-subgroups have normal series of length k all of whose quotients belong to 𝔛(n). We show that the non-p-soluble length λp(G) of G is bounded in terms of k and n only (Theorem 1.2). In the case where p is odd, a stronger result is obtained (Theorem 1.3). 相似文献
6.
In Theorem 1, letting p be a prime, we prove: (1) If G=Sn is a symmetric group of degree n, then G contains two Sylow p-subgroups with trivial intersection iff (p, n) ∉ {(3, 3), (2,
2), (2, 4), (2, 8)}, and (2) If H=An is an alternating group of degree n, then H contains two Sylow p-subgroups with trivial intersection iff (p, n) ∉ {(3, 3),
(2, 4)}. In Theorem 2, we argue that if G is a finite simple non-Abelian group and p is a prime, then G contains a pair of
Sylow p-subgroups with trivial intersection. Also we present the corollary which says that if P is a Sylow subgroup of a finite
simple non-Abelian group G, then ‖G‖>‖P‖2.
Supported by RFFR grants Nos. 93-01-01529, 93-01-01501, and 96-01-01893, and by International Science Foundation and Government
of Russia grant RPC300.
Translated fromAlgebra i Logika, Vol. 35, No. 4, pp. 424–432, July–August, 1996. 相似文献
7.
Robert M. Guralnick 《Proceedings of the American Mathematical Society》2007,135(3):689-693
We show that if is a reductive group, then th roots of conjugacy classes are a finite union of conjugacy classes, and that if is an algebraic overgroup of , then the intersection of with a conjugacy class of is a finite union of -conjugacy classes. These results follow from results on finiteness of unipotent classes in an almost simple algebraic group.
8.
9.
A subgroup H of a group G is called s-conditionally permutable in G if for every Sylow subgroup T of G there exists an element x ∈ G such that HTx = TxH. Using the concept of s-conditionally permutable subgroups, some new characterizations of finite groups are obtained and several interesting results are generalized. 相似文献
10.
LI JinBao CHEN GuiYun & CHEN RuiFang School of Mathematics Statistics Southwest University Chongqing China 《中国科学 数学(英文版)》2011,(9)
Let H be a subgroup of a group G.Then H is said to be S-quasinormal in G if HP = P H for every Sylow subgroup P of G;H is said to be S-quasinormally embedded in G if a Sylow p-subgroup of H is also a Sylow p-subgroup of some S-quasinormal subgroup of G for each prime p dividing the order of H.In this paper,we say that H is weakly S-embedded in G if G has a normal subgroup T such that HT is an S-quasinormal subgroup of G and H ∩ T≤H SE,where H SE denotes the subgroup of H generated by all those subgroups of ... 相似文献
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12.
设G为有限群,称G的子群H为ss-置换子群,如果存在G的次正规子群B使得G=HB,且H与B的任意Sylow子群可以交换,即对任意X∈Syl(B)有XH=HX.利用子群的ss-置换性来研究有限群的结构,得到有限群超可解的两个充分条件. 相似文献
13.
In this paper, we investigate the finite groups all of whose non-normal nilpotent subgroups are cyclic. We show that such groups are solvable with cyclic centers. If G is a non-supersolvable group, then G has only one non-cyclic Sylow subgroup which is either isomorphic to Q8 or is of type (q, q). 相似文献
14.
Adam J. Prze
dziecki 《Journal of Algebra》2008,320(12):4270-4280
We construct examples of localizations in the category of groups which take the Mathieu group M11 to groups of arbitrarily large cardinality which are “abelian up to finitely many generators.” The paper is part of a broader study on the group theoretic properties which are or are not preserved by localizations. 相似文献
15.
In this paper we study the influence of the partial cover and avoidance property on the subgroups of some relevant families of subgroups in a finite group. 相似文献
16.
A subgroup H of a finite group G is said to be an SS-quasinormal subgroup of G if there is a subgroup B of G such that G = HB and H permutes with every Sylow subgroup of B. In this paper, we investigate the structure of a group under the assumption that every subgroup with order pm of a Sylow p-subgroup P of G is SS-quasinormal in G for a fixed positive integer m. Some interesting results related to the p-nilpotency and supersolvability of a finite group are obtained. For example, we prove that G is p-nilpo... 相似文献
17.
V. V. Shlyk 《Mathematical Notes》1973,14(3):804-809
The intersections of maximal subgroups of a definite kind in finite groups are investigated. In particular, it is proved that the intersection of all noninvariant nonnilpotent maximal subgroups is nilpotent in a finite nonsolvable group.Translated from Matematicheskie Zametki, Vol. 14, No. 3, pp. 429–439, September, 1973. 相似文献
18.
Selçuk Kayacan 《代数通讯》2018,46(4):1492-1505
The intersection graph of a group G is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper non-trivial subgroups of G, and there is an edge between two distinct vertices H and K if and only if H∩K≠1 where 1 denotes the trivial subgroup of G. In this paper, we classify finite solvable groups whose intersection graphs are not 2-connected and finite nilpotent groups whose intersection graphs are not 3-connected. Our methods are elementary. 相似文献
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20.
We call a subgroup H of a finite group G c-supplemented in G if there exists a subgroup K of G such that G = HK and H ∩ K ≤ core(H). In this paper it is proved that a finite group G is p-nilpotent if G is S4-free and every minimal subgroup of P n GN is c-supplemented in NG(P), and when p = 2 P is quaternion-free, where p is the smallest prime number dividing the order of G, P a Sylow p-subgroup of G. As some applications of this result, some known results are generalized. 相似文献