Finite Groups with a Given Set of Character Degrees

Shafiei, Farideh; Iranmanesh, Ali; Lewis, Mark L.; Aziziheris, Kamal

doi:10.1007/s10468-015-9576-1

Cited by 3 publications

(3 citation statements)

References 20 publications

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“…Example 2.5. We recall a construction from [29]. Let p, q, and r be three, not necessarily distinct, primes with q = r such that q and r do not divide p qr − 1, let V be the additive group of the field F p qr of order p qr , let S be the Galois group of the field extension F p qr /F p , let C be the cyclic subgroup of order p qr −1 p r −1 of the multiplicative group of F * p qr and let G :…”

Section: Groups Whose Bipartite Divisor Graphs Have Special Shapesmentioning

confidence: 99%

“…Thus B(G) is a path if and only if p qr −1 p r −1 is a prime power. Lemma 3.1 in [29] yields that, if p qr −1 p r −1 is a prime power, then either r is a power of q, or p = q = 2 and r = 3. The first case is not possible because by hypothesis r and q are distinct primes.…”

Section: Groups Whose Bipartite Divisor Graphs Have Special Shapesmentioning

confidence: 99%

“…and α 3 , where α 1 := (1, 2)(3, 14, 9, 20)(4, 15, 19, 27)(5, 7)(6, 8)(10, 21, 18, 26)(11, 22, 12, 23)(13, 16)(17, 31, 25, 29)(24, 32, 28, 30), α 2 := (2, 27, 25, 19, 21, 10, 31)(3,29,8,22,17,11,14)(4,20,9,30,16,15,24)(7,23,28,12,26,18,32),…”

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On regular bipartite divisor graph for the set of irreducible character degrees

Hafezieh¹

2018

HJMS

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Let G be a finite group. The bipartite divisor graph B(G) for the set of irreducible complex character degrees cd(G) is the undirected graph with vertex set consisting of the prime numbers dividing some element of cd(G) and of the non-identity character degrees in cd(G), where a prime number p is declared to be adjacent to a character degree m if and only if p divides m. The graph B(G) is bipartite and it encodes two of the most widely studied graphs associated to the character degrees of a finite group: the prime graph and the divisor graph on the set of irreducible character degrees.

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Section: Groups Whose Bipartite Divisor Graphs Have Special Shapesmentioning

confidence: 99%

Section: Groups Whose Bipartite Divisor Graphs Have Special Shapesmentioning

confidence: 99%

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On regular bipartite divisor graph for the set of irreducible character degrees

Hafezieh¹

2018

HJMS

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The character co-degree sets and solvability

2023

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For a character [Formula: see text] of a finite group [Formula: see text], the number [Formula: see text] is called the co-degree of [Formula: see text]. In this paper, we concentrate on some conditions on the character co-degree sets implying solvability. More precisely, we show that if for every non-principal irreducible characters [Formula: see text] and [Formula: see text] of [Formula: see text] with [Formula: see text], the greatest common divisor of [Formula: see text] and [Formula: see text] is divisible by at most two primes (counting multiplicities), then either [Formula: see text] is solvable or [Formula: see text] is isomorphic to one of the groups [Formula: see text], [Formula: see text] or an extension of an elementary abelian [Formula: see text]-group [Formula: see text] of order [Formula: see text] by [Formula: see text]. In the last case, the set of the co-degrees of the irreducible characters of [Formula: see text] is [Formula: see text].

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An overview on the bipartite divisor graph for the set of irreducible character degrees

Hafezieh¹,

Spiga²

2020

Rocky Mountain J. Math.

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Finite Groups with a Given Set of Character Degrees

Cited by 3 publications

References 20 publications

On regular bipartite divisor graph for the set of irreducible character degrees

On regular bipartite divisor graph for the set of irreducible character degrees

The character co-degree sets and solvability

An overview on the bipartite divisor graph for the set of irreducible character degrees

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