Character separation and principal covering

Bessenrodt, Christine; Zhang, Jiping

doi:10.1016/j.jalgebra.2010.10.034

Cited by 4 publications

(3 citation statements)

References 17 publications

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“…At last, we also obtain some results about nilpotent properties of Frobenius corresponding blocks. These results partly answer some questions in paper [13] [14].…”

Section: Introductionsupporting

confidence: 77%

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Block Form of Frobenius Groups

Zeng¹,

Zhang²

2020

Preprint

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The aim of this paper is to apply character properties of Frobenius group to a local block form of an group algebra. We start by establishing a block form of Brauer permutation Lemma by using block participation of conjugate classes of a group G. Then we can define a pair of Frobenius corresponding blocks between a group G and its normal subgroup N . A near group condition is given to determine a pair of Frobenius corresponding blocks. With a pair of Frobenius corresponding blocks, we study its group structure. At last we prove connections between nilpotent properties and Frobenius corresponding blocks.

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“…At last, we also obtain some results about nilpotent properties of Frobenius corresponding blocks. These results partly answer some questions in paper [13] [14].…”

Section: Introductionsupporting

confidence: 77%

“…The following result is related to their question. According to results in [15, X, Theorem 1.5, P416] and [14], we are going to prove the following result: Theorem 6.4. Let N G and G/N is solvable.…”

mentioning

confidence: 99%

Block Form of Frobenius Groups

Zeng¹,

Zhang²

2020

Preprint

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“…For instance, Bessenrodt, Malle and Olsson [BMO06] introduced the concept of block separability of characters, and Navarro, Turull and Wolf [NTW05] discussed solvable groups that are block separated. In a series of papers, Bessenrodt and Zhang generally investigated block separations, inclusions and coverings of characters of a finite group, see [BZ08] and [BZ11]. Motivated by their work, we investigate block separations of characters from a graph-theoretical point of view.…”

Section: Introductionmentioning

confidence: 99%

The block graph of a finite group

Brough,

Liu,

Paolini

2017

Preprint

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This paper studies intersections of principal blocks of a finite group with respect to different primes. We first define the block graph of a finite group G, whose vertices are the prime divisors of |G| and there is an edge between two vertices p = q if and only if the principal p-and q-blocks of G have a nontrivial common complex irreducible character of G. Then we determine the block graphs of finite simple groups, which turn out to be complete except those of J 1 and J 4 . Also, we determine exactly when the Steinberg character of a finite simple group of Lie type lies in a principal block. Based on the above investigation, we obtain a criterion for the p-solvability of a finite group which in particular leads to an equivalent condition for the solvability of a finite group. Thus, together with two recent results of Bessenrodt and Zhang, the nilpotency, p-nilpotency and solvability of a finite group can be characterized by intersections of principal blocks of some quotient groups.

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Finite groups whose irreducible characters of principal blocks have prime power degrees

Liu

2015

Monatsh Math

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Character separation and principal covering

Cited by 4 publications

References 17 publications

Block Form of Frobenius Groups

Block Form of Frobenius Groups

The block graph of a finite group

Finite groups whose irreducible characters of principal blocks have prime power degrees

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