共查询到20条相似文献,搜索用时 0 毫秒
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Marius Tărnăuceanu 《Mathematica Slovaca》2014,64(2):311-314
In this note we give a characterization of finite groups of order pq 3 (p, q primes) that fail to satisfy the Converse of Lagrange’s Theorem. 相似文献
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Anthony Bak 《Topology》1975,14(4):367-374
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Alexandre Turull 《Journal of Algebra》2008,319(2):739-758
Let G be a finite solvable group, p be some prime, let P be a Sylow p-subgroup of G, and let N be its normalizer in G. Assume that N has odd order. Then, we prove that there exists a bijection from the set of all irreducible characters of G of degree prime to p to the set of all the irreducible characters of degree prime to p of N such that it preserves ± the degree modulo p, the field of values, and the Schur index over every field of characteristic zero. This strengthens a more general recent result [A. Turull, Character correspondences in solvable groups, J. Algebra 295 (2006) 157–178], but only for the case under consideration here. In addition, we prove some other strong character correspondences that have very good rationality properties. As one consequence, we prove that a solvable group G has a non-trivial rational irreducible character with degree prime to p if and only if the order of the normalizer of a Sylow p-subgroup of G has even order. 相似文献
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An Abelian group or module is said to have the involution property if every endomorphism is the sum of two automorphisms, one of which is an involution. We investigate this property for completely decomposable torsion-free Abelian groups and modules over the ring of p-adic integers. 相似文献
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R. Julian R. Abel Diana Combe Adrian M. Nelson William D. Palmer 《Designs, Codes and Cryptography》2013,69(2):189-201
We show that the established necessary conditions for a GBRD ${(v,3,\lambda; \mathbb {G})}$ are sufficient (i) when ${\mathbb {G}}$ is supersolvable and (ii) when ${\mathbb {G}}$ is solvable with ${\vert \mathbb {G} \vert }$ prime to 3. 相似文献
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Let G be a finite group, and let Cay(G, S) be a Cayley digraph of G. If, for all T ⊂ G, Cay(G, S) ≅ Cay(G, T) implies Sα = T for some α ∈ Aut(G), then Cay(G, S) is called a CI-graph of G. For a group G, if all Cayley digraphs of valency m are CI-graphs, then G is said to have the m-DCI property; if all Cayley graphs of valency m are CI-graphs, then G is said to have the m-CI property. It is shown that every finite group of order greater than 2 has a nontrivial CI-graph, and all finite groups with the m-CI property and with the m-DCI property are characterized for small values of m. A general investigation is made of the structure of Sylow subgroups of finite groups with the m-DCI property and with the m-CI property for large values of m. © 1998 John Wiley & Sons, Inc. J Graph Theory 27: 21–31, 1998 相似文献
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Luca Fabrizio Di Cerbo 《Geometriae Dedicata》2009,143(1):193-199
We provide a lower bound for the uniform exponential growth rate of closed nonflat nonpositively curved 3-manifold groups.
A detailed study of the uniform exponential growth rate of closed 3-manifold groups is also presented. 相似文献
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n this paper, we study the structure of polycyclic groups admitting an automorphism of order four on the basis of Neumann’s result, and prove that if α is an automorphism of order four of a polycyclic group G and the map φ: G → G defined by gφ = [g,α] is surjective, then G contains a characteristic subgroup H of finite index such that the second derived subgroup H″ is included in the centre of H and CH(α2) is abelian, both CG(α2) and G/[G, α2] are abelian-by-finite. These results extend recent and classical results in the literature. 相似文献
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Pavel Shumyatsky 《Proceedings of the American Mathematical Society》1999,127(9):2583-2586
Let be a prime, a non-negative integer. We prove that if is a residually finite group such that for all , then is locally finite.