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11.
12.
Let G be a finite group, Irr1(G) be the set of nonlinear irreducible characters of G and cd1(G) the set of degrees of the characters in Irr1(G). A group G is said to be a D2-group if|cd1(G)|=|Irr1(G)|-2. In this paper, we give a complete classification of solvable D2-groups. 相似文献
13.
Tobias Kildetoft 《代数通讯》2017,45(6):2325-2333
We define the position of an irreducible complex character of a finite group as an alternative to the degree. We then use this to define three classes of groups: position reducible (PR)-groups, inductively position reducible (IPR)-groups and weak IPR-groups. We show that IPR-groups and weak IPR-groups are solvable and satisfy the Taketa inequality (ie, that the derived length of the group is at most the number of degrees of irreducible complex characters of the group), and we show that any M-group is a weak IPR-group. We also show that even though PR-groups need not be solvable, they cannot be perfect. 相似文献
14.
Simon R. Blackburn 《Discrete Mathematics》2006,306(12):1126-1131
We obtain upper bounds on character sums and autocorrelation of nonlinear recurrence sequences over arbitrary finite rings. 相似文献
15.
Alexander Moretó 《Algebras and Representation Theory》2007,10(4):333-338
Given a group G, Γ(G) is the graph whose vertices are the primes that divide the degree of some irreducible character and two vertices p and q are joined by an edge if pq divides the degree of some irreducible character of G. By a definition of Lewis, a graph Γ has bounded Fitting height if the Fitting height of any solvable group G with Γ(G)=Γ is bounded (in terms of Γ). In this note, we prove that there exists a universal constant C such that if Γ has bounded Fitting height and Γ(G)=Γ then h(G)≤C. This solves a problem raised by Lewis.
Research supported by the Spanish Ministerio de Educación y Ciencia, MTM2004-06067-C02-01 and MTM2004-04665, the FEDER and
Programa Ramón y Cajal. 相似文献
16.
Greg McShane introduced a remarkable identity for lengths of simple closed geodesics on the once punctured torus with a complete, finite volume hyperbolic structure. Bowditch later generalized this and gave sufficient conditions for the identity to hold for general type-preserving representations of a free group on two generators Γ to SL(2,C), this was further generalized by the authors to obtain sufficient conditions for a generalized McShane’s identity to hold for arbitrary (not necessarily type-preserving) non-reducible representations in Tan et al. (Submitted). Here we extend the above by giving necessary and sufficient conditions for the generalized McShane identity to hold (Akiyoshi, Miyachi and Sakuma had proved it for type-preserving representations). We also give a version of Bowditch’s variation of McShane’s identity to once-punctured torus bundles, in the case where the monodromy is generated by a reducible element, and provide necessary and sufficient conditions for the variations to hold. 相似文献
17.
Sandro Mattarei 《Proceedings of the American Mathematical Society》2006,134(8):2189-2195
We prove that knowledge of the character degrees of a finite group and of their multiplicities determines whether has a Sylow -subgroup as a direct factor. An analogous result based on knowledge of the conjugacy class sizes is known. We prove variations of both results and discuss their similarities.
18.
We introduce notions of absolutely non-free and perfectly non-free group actions and use them to study the associated unitary representations. We show that every weakly branch group acting on a regular rooted tree acts absolutely non-freely on the boundary of the tree. Using this result and the symmetrized diagonal actions we construct for every countable branch group infinitely many different ergodic perfectly non-free actions, infinitely many II1-factor representations, and infinitely many continuous ergodic invariant random subgroups. 相似文献
19.
In this paper, we use character-theoretic techniques to give new nonexistence results for -strong external difference families (SEDFs). We also use cyclotomic classes to give two new classes of SEDFs with . 相似文献
20.
Structures of table algebras determined by their character tables are studied in [6]. In this paper we continue the research in this direction. In particular, we investigate the conditions under which the character table with a zero submatrix yields a generalized wreath product for a commutative table algebra. Applications to finite groups are also discussed, and some new and known results are obtained as direct consequences. 相似文献