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Добірка наукової літератури з теми "CHARACTER THEORY, FINITE GROUPS"

Автор: Grafiati

Опубліковано: 10 березня 2023

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Статті в журналах з теми "CHARACTER THEORY, FINITE GROUPS"

1

Boyer, Robert. "Character theory of infinite wreath products." International Journal of Mathematics and Mathematical Sciences 2005, no. 9 (2005): 1365–79. http://dx.doi.org/10.1155/ijmms.2005.1365.

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The representation theory of infinite wreath product groups is developed by means of the relationship between their group algebras and conjugacy classes with those of the infinite symmetric group. Further, since these groups are inductive limits of finite groups, their finite characters can be classified as limits of normalized irreducible characters of prelimit finite groups. This identification is called the “asymptotic character formula.” TheK0-invariant of the groupC∗-algebra is also determined.

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2

Isaacs, I. M. "The π-character theory of solvable groups". Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 57, № 1 (1994): 81–102. http://dx.doi.org/10.1017/s1446788700036077.

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AbstractThere is a deeper structure to the ordinary character theory of finite solvable groups than might at first be apparent. Mauch of this structure, which has no analog for general finite gruops, becomes visible onyl when the character of solvable groups are viewes from the persepective of a particular set π of prime numbers. This purely expository paper discusses the foundations of this πtheory and a few of its applications. Included are the definitions and essential properties of Gajendragadkar's π-special characters and their connections with the irreducible πpartial characters and their associated Fong characters. Included among the consequences of the theory discussed here are applications to questions about the field generated by the values of a character, about extensions of characters of subgroups and about M-groups.

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3

Isaacs, I. M. "Book Review: Character theory of finite groups." Bulletin of the American Mathematical Society 36, no. 04 (1999): 489–93. http://dx.doi.org/10.1090/s0273-0979-99-00789-2.

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4

Ikeda, Kazuoki. "Character Values of Finite Groups." Algebra Colloquium 7, no. 3 (2000): 329–33. http://dx.doi.org/10.1007/s10011-000-0329-1.

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5

Chetard, Béatrice I. "Graded character rings of finite groups." Journal of Algebra 549 (May 2020): 291–318. http://dx.doi.org/10.1016/j.jalgebra.2019.11.041.

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6

Schmid, Peter. "Finite groups satisfying character degree congruences." Journal of Group Theory 21, no. 6 (2018): 1073–94. http://dx.doi.org/10.1515/jgth-2018-0019.

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Abstract Let G be a finite group, p a prime and {c\in\{0,1,\ldots,p-1\}} . Suppose that the degree of every nonlinear irreducible character of G is congruent to c modulo p. If here {c=0} , then G has a normal p-complement by a well known theorem of Thompson. We prove that in the cases where {c\neq 0} the group G is solvable with a normal abelian Sylow p-subgroup. If {p\neq 3} then this is true provided these character degrees are congruent to c or to {-c} modulo p.

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7

Xiong, Huan. "Finite Groups Whose Character Graphs Associated with Codegrees Have No Triangles." Algebra Colloquium 23, no. 01 (2016): 15–22. http://dx.doi.org/10.1142/s1005386716000031.

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Motivated by Problem 164 proposed by Y. Berkovich and E. Zhmud' in their book “Characters of Finite Groups”, we give a characterization of finite groups whose irreducible character codegrees are prime powers. This is based on a new kind of character graphs of finite groups associated with codegrees. Such graphs have close and obvious connections with character codegree graphs. For example, they have the same number of connected components. By analogy with the work of finite groups whose character graphs (associated with degrees) have no triangles, we conduct a result of classifying finite groups whose character graphs associated with codegrees have no triangles in the latter part of this paper.

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8

Madanha, Sesuai Yash. "Zeros of primitive characters of finite groups." Journal of Group Theory 23, no. 2 (2020): 193–216. http://dx.doi.org/10.1515/jgth-2019-2051.

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AbstractWe classify finite non-solvable groups with a faithful primitive irreducible complex character that vanishes on a unique conjugacy class. Our results answer a question of Dixon and Rahnamai Barghi and suggest an extension of Burnside’s classical theorem on zeros of characters.

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9

Qian, Guohua. "Finite groups with consecutive nonlinear character degrees." Journal of Algebra 285, no. 1 (2005): 372–82. http://dx.doi.org/10.1016/j.jalgebra.2004.11.021.

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10

Chillag, David, and Marcel Herzog. "Finite groups with almost distinct character degrees." Journal of Algebra 319, no. 2 (2008): 716–29. http://dx.doi.org/10.1016/j.jalgebra.2005.07.039.

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