共查询到20条相似文献,搜索用时 15 毫秒
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W. Willems 《Transactions of the American Mathematical Society》2005,357(6):2379-2387
Based on a large amount of examples, which we have checked so far, we conjecture that where is a prime and the sum runs through the set of irreducible Brauer characters in characteristic of the finite group . We prove the conjecture simultaneously for -solvable groups and groups of Lie type in the defining characteristic. In non-defining characteristics we give asymptotically an affirmative answer in many cases.
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In this paper we study groups for which every real irreducible character has degree not divisible by some given odd prime p. 相似文献
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Yang LIU 《Frontiers of Mathematics in China》2022,17(6):1083
Let G be a nonsolvable group and Irr(G) the set of irreducible complex characters of G. We consider the nonsolvable groups whose character degrees have special 2-parts and prove that if χ(1)2 = 1 or |G|2 for every χ ∈ Irr(G), then there exists a minimal normal subgroup N of G such that N ≅ PSL(2, 2n) and G/N is an odd order group. 相似文献
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We describe the structure of the finite groups in which the sizes of noncentral conjugacy classes have the same p-part, for some prime p. We prove that they are solvable, they have a normal p-complement and their Fitting length is at most three. 相似文献
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Udo Leisering 《Archiv der Mathematik》1990,55(4):324-332
This is a part of a doctoral-thesis at Mainz. The author thanks the Deutsche Forschungsge-meinschaft for its support. 相似文献
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We classify the finite groups which satisfy the condition that any two nonprincipal complex irreducible characters of the same degree are Galois conjugate. 相似文献
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In the literature, there are several graphs related to a finite group G. Two of them are the character degree graph, denoted by ΔG), and the prime graph ΓG), In this paper we classify all finite groups whose character degree graphs are disconnected and coincide with their prime graphs. As a corollary, we find all finite groups whose character degree graphs are square and coincide with their prime graphs. 相似文献
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We study the structure of finite groups whosemaximal subgroups have the Hall property. We prove that such a group G has at most one non-Abelian composition factor, the solvable radical S(G) admits a Sylow series, the action of G on sections of this series is irreducible, the series is invariant with respect to this action, and the quotient group G/S(G) is either trivial or isomorphic to PSL2(7), PSL2(11), or PSL5(2). As a corollary, we show that every maximal subgroup of G is complemented. 相似文献
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In this note we classify the finite groups satisfying the following property P5: their conjugacy class lengths are set-wise relatively prime for any 5 distinct classes.Received: 6 October 2004; revised: 16 November 2004 相似文献
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O. A. Alekseeva A. S. Kondrat’ev 《Proceedings of the Steklov Institute of Mathematics》2016,295(1):11-20
Finite groups whose prime graphs do not contain triangles are investigated. In the present part of the study, the isomorphic types of prime graphs and estimates of the Fitting length of solvable groups are found and almost simple groups are determined. 相似文献
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Amin Saeidi 《Quaestiones Mathematicae》2016,39(4):523-530
In this paper, we study finite 2-groups in which distinct nonlinear irreducible characters have distinct kernels. We prove several results concerning these groups and completely classify 2-groups with at most five nonlinear irreducible characters satisfying this property. 相似文献
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A finite group G all of whose nonlinear irreducible characters are rational is called a
\mathbbQ1{\mathbb{Q}_1}-group. In this paper, we obtain some results concerning the structure of
\mathbbQ1{\mathbb{Q}_1}-groups. 相似文献
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Summary Beynon and Lusztig have shown that the fake degrees of almost all irreducible characters of finite real reflection groups are palindromes, and that the exceptions to this rule correspond to the non rational characters of the generic ringA defined overR=C[q]. Their proof consists of a case-by-case check. In this note we give an explanation for this phenomenon and some related facts about fake degrees. Moreover, in the situation where we allow for distinct parametersq
in the definition ofA, we shall give a simple uniform proof of the fact that all the central idempotents of
are elements of
, where
.Oblatum 10-XI-1994 相似文献
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In [2] we proved that ifG is a finite group containing an involution whose centralizer has order bounded by some numberm, thenG contains a nilpotent subgroup of class at most two and index bounded in terms ofm. One of the steps in the proof of that result was to show that ifG is soluble, then ¦G/F(G) ¦ is bounded by a function ofm, where F (G) is the Fitting subgroup ofG. We now show that, in this part of the argument, the involution can be replaced by an arbitrary element of prime order. 相似文献