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1.
A proper subgroup H of a group G is said to be strongly embedded if 2 (H) and 2(HH
g) (for all
). An involution i of G is said to be finite if
(for all g G). As is known, the structure of a (locally) finite group possessing a strongly embedded subgroup is determined by the theorems of Burnside and Brauer--Suzuki, provided that the Sylow 2-subgroup contains a unique involution. In this paper, sufficient conditions for the equality m
2(G)= 1 are established, and two analogs of the Burnside and Brauer—Suzuki theorems for infinite groups G possessing a strongly embedded subgroup and a finite involution are given. 相似文献
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Guohua Qian 《代数通讯》2013,41(12):4514-4519
The aim of this note is to classify the finite groups with unique n-maximal subgroup. 相似文献
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本文研究所有子群皆交换或正规的有限群. 我们获得了非幂零的情形的一个特征刻画, 也给出了幂零情形的一些性质. 相似文献
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Let p be a prime, k an algebraically closed field ofcharacteristic p, and G a finite group with a Sylowp-Subgroup P. In this paper, we consider the property thatNG(P)/P is Abelian. We provide somenecessary or sufficient conditions NG(P)/P to be Abelian in term of thestructure of the group algebra kG as a k-algebra, in casethat G is p-nilpotent or of p-length 1. 相似文献
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The goal of this article is to study finite groups admitting a pseudocomplemented subgroup lattice (PK-groups) or a pseudocomplemented normal subgroup lattice (PKN-groups). In particular, we obtain a complete classification of finite PK-groups and of finite nilpotent PKN-groups. We also study groups with a Stone normal subgroup lattice, and we classify finite groups for which every subgroup has a Stone normal subgroup lattice. Finally, we obtain a complete classification of finite groups for which every subgroup is monolithic. 相似文献
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A proper subgroup H of a group G is said to be strongly isolated if it contains the centralizer of any nonidentity element of H and 2-isolated if the conditions >C
G(g) H 1 and 2(CG(g)) imply that CG(g)H. An involution i in a group G is said to be finite if |ii
g| < (for any g G). In the paper we study a group G with finite involution i and with a 2-isolated locally finite subgroup H containing an involution. It is proved that at least one of the following assertions holds:1) all 2-elements of the group G belong to H;2) (G,H) is a Frobenius pair, H coincides with the centralizer of the only involution in H, and all involutions in G are conjugate;3) G=FFCG(i) is a locally finite Frobenius group with Abelian kernel F;4) H=V D is a Frobenius group with locally cyclic noninvariant factor D and a strongly isolated kernel V, U=O2(V) is a Sylow 2-subgroup of the group G, and G is a Z-group of permutations of the set =U
g g G. 相似文献
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Let X be a nonempty subset of a group G.A subgroup H of G is said to be X-s-permutable in G if there exists an element x ∈ X such that HPx = PxH for every Sylow subgroup P of G.In this paper,some new results are given under the assumption that some suited subgroups of G are X-s-permutable in G. 相似文献
12.
设G为有限群, 如果G的每个非2-闭极大子群的指数均为素数幂, 那么
G-S(G)≌PSL2(7)或1, 其中S(G)为G的最大可解正规子群. 相似文献
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The Dual Group of a Dense Subgroup 总被引:1,自引:1,他引:0
W. W. Comfort S. U. Raczkowski F. Javier Trigos-Arrieta 《Czechoslovak Mathematical Journal》2004,54(2):509-533
Throughout this abstract, G is a topological Abelian group and $\hat G$ is the space of continuous homomorphisms from G into the circle group ${\mathbb{T}}$ in the compact-open topology. A dense subgroup D of G is said to determine G if the (necessarily continuous) surjective isomorphism $\hat G \to \hat D$ given by $h \mapsto h\left| D \right.$ is a homeomorphism, and G is determined if each dense subgroup of G determines G. The principal result in this area, obtained independently by L. Außenhofer and M. J. Chasco, is the following: Every metrizable group is determined. The authors offer several related results, including these. 1. There are (many) nonmetrizable, noncompact, determined groups. 2. If the dense subgroup D i determines G i with G i compact, then $ \oplus _i D_i $ determines Πi G i. In particular, if each G i is compact then $ \oplus _i G_i $ determines Πi G i. 3. Let G be a locally bounded group and let G + denote G with its Bohr topology. Then G is determined if and only if G + is determined. 4. Let non $\left( {\mathcal{N}} \right)$ be the least cardinal κ such that some $X \subseteq {\mathbb{T}}$ of cardinality κ has positive outer measure. No compact G with $w\left( G \right) \geqslant non\left( {\mathcal{N}} \right)$ is determined; thus if $\left( {\mathcal{N}} \right) = {\mathfrak{N}}_1 $ (in particular if CH holds), an infinite compact group G is determined if and only if w(G) = ω. Question. Is there in ZFC a cardinal κ such that a compact group G is determined if and only if w(G) < κ? Is $\kappa = non\left( {\mathcal{N}} \right)?\kappa = {\mathfrak{N}}_1 ?$ 相似文献
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设R是一个主理想整环,GL(n,R)为R上n阶一般线性群,H_r为GL(n,R)的一个子群,在n≥3的情形下给出H_r在GL(n,R)中的所有扩群. 相似文献
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We prove that certain hyperbolic Coxeter groups are separable on their geometrically finite subgroups. 相似文献
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The aim of this article is to give a generalization of the concept of commutativity degree of a finite group G (denoted by d(G)), to the concept of relative commutativity degree of a subgroup H of a group G (denoted by d(H, G)). We shall state some results concerning the new concept which are mostly new or improvements of known results given in Gustafson (1973) and Moghaddam et al. (2005). Moreover, we shall define the relative nth nilpotency degree of a subgroup of a group and give some results concerning this at the end of the article. 相似文献