共查询到20条相似文献,搜索用时 46 毫秒
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Achim Tresch 《Journal of Pure and Applied Algebra》2007,208(1):331-338
For a group class X, a group G is said to be a CX-group if the factor group G/CG(gG)∈X for all g∈G, where CG(gG) is the centralizer in G of the normal closure of g in G. For the class Ff of groups of finite order less than or equal to f, a classical result of B.H. Neumann [Groups with finite classes of conjugate elements, Proc. London Math. Soc. 1 (1951) 178-187] states that if G∈CFf, the commutator group G′ belongs to Ff′ for some f′ depending only on f. We prove that a similar result holds for the class , the class of soluble groups of derived length at most d which have Prüfer rank at most r. Namely, if , then for some r′ depending only on r. Moreover, if , then for some r′ and f′ depending only on r,d and f. 相似文献
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Su Gao 《Advances in Mathematics》2008,217(2):814-832
A group G?Sym(N) is cofinitary if g has finitely many fixed points for every g∈G except the identity element. In this paper, we discuss the definability of maximal cofinitary groups and some related structures. More precisely, we show the following two results:
- (1)
- Assuming V=L, there is a set of permutations on N which generates a maximal cofinitary group.
- (2)
- Assuming V=L, there is a mad permutation family in Sym(N).
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S.V. Ivanov 《Advances in Mathematics》2008,218(2):465-484
The Kurosh rank rK(H) of a subgroup H of a free product of groups Gα, α∈I, is defined accordingly to the classic Kurosh subgroup theorem as the number of free factors of H. We prove that if H1, H2 are subgroups of and H1, H2 have finite Kurosh rank, then , where , q∗ is the minimum of orders >2 of finite subgroups of groups Gα, α∈I, q∗:=∞ if there are no such subgroups, and if q∗=∞. In particular, if the factors Gα, α∈I, are torsion-free groups, then . 相似文献
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Let H be a torsion-free strongly polycyclic (torsion-free virtually polycyclic, resp.) group. Let G be any group with maximal condition. We show that there exists a torsion-free strongly polycyclic (torsion-free virtually polycyclic, resp.) group and an epimorphism such that for any homomorphism ?:G→H, it factors through , i.e., there exists a homomorphism such that . We show that this factorization property cannot be extended to any finitely generated group G. As an application of factorization, we give necessary and sufficient conditions for N(f,g)=R(f,g) to hold for maps f,g:X→Y between closed orientable n-manifolds where π1(X) has the maximal condition, Y is an infra-solvmanifold, N(f,g) and R(f,g) denote the Nielsen and Reidemeister coincidence numbers, respectively. 相似文献
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In this paper, we show that, for every locally compact abelian group G, the following statements are equivalent:
- (i)
- G contains no sequence such that {0}∪{±xn∣n∈N} is infinite and quasi-convex in G, and xn?0;
- (ii)
- one of the subgroups {g∈G∣2g=0} or {g∈G∣3g=0} is open in G;
- (iii)
- G contains an open compact subgroup of the form or for some cardinal κ.
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Nikolai Gordeev 《Journal of Pure and Applied Algebra》2009,213(2):250-258
We obtain the following characterization of the solvable radical R(G) of any finite group G: R(G) coincides with the collection of all g∈G such that for any 3 elements a1,a2,a3∈G the subgroup generated by the elements , i=1,2,3, is solvable. In particular, this means that a finite group G is solvable if and only if in each conjugacy class of G every 4 elements generate a solvable subgroup. The latter result also follows from a theorem of P. Flavell on {2,3}′-elements in the solvable radical of a finite group (which does not use the classification of finite simple groups). 相似文献
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Jiehua Mai 《Topology and its Applications》2007,154(11):2306-2311
Let G be a graph and be continuous. Denote by P(f), , ω(f) and Ω(f) the set of periodic points, the closure of the set of periodic points, ω-limit set and non-wandering set of f, respectively. In this paper we show that: (1) v∈ω(f) if and only if v∈P(f) or there exists an open arc L=(v,w) contained in some edge of G such that every open arc U=(v,c)⊂L contains at least 2 points of some trajectory; (2) v∈ω(f) if and only if every open neighborhood of v contains at least r+1 points of some trajectory, where r is the valence of v; (3) ; (4) if , then x has an infinite orbit. 相似文献
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Julie Yeramian 《Journal of Pure and Applied Algebra》2009,213(6):1013-1025
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Moritz Jirak 《Journal of multivariate analysis》2011,102(6):1032-1046
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Christopher Mouron 《Topology and its Applications》2009,156(3):558-576
Suppose that is a collection of disjoint subcontinua of continuum X such that limi→∞dH(Yi,X)=0 where dH is the Hausdorff metric. Then the following are true:
- (1)
- X is non-Suslinean.
- (2)
- If each Yi is chainable and X is finitely cyclic, then X is indecomposable or the union of 2 indecomposable subcontinua.
- (3)
- If X is G-like, then X is indecomposable.
- (4)
- If all lie in the same ray and X is finitely cyclic, then X is indecomposable.
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Daniel S. Farley 《Topology》2003,42(5):1065-1082
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