The unitary cover of a finite group and the exponent of the Schur multiplier

Sambonet, Nicola

doi:10.1016/j.jalgebra.2014.12.013

Cited by 14 publications

(9 citation statements)

References 17 publications

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“…In the next Theorem, we show that to prove the conjecture for regular p-groups, it is enough to prove it for groups of exponent p. This result also appears in [25]. But here, we prove it more generally for the exterior square.…”

Section: (I) [Gh Gh Gh Gh H] = [H H H G H][h H G G H][h G H G H][g H ...mentioning

confidence: 59%

“…when exp(G) is even. Using our techniques, we obtain the following generalization of Theorem A of [25], which is one of their main results. Theorem 6.3.…”

Section: Introductionmentioning

confidence: 94%

“…In [19], P. Moravec showed that if d is the derived length of G, then exp(M(G)) | (exp(G)) 2(d−1) . The author of [25] improved this bound by proving that exp(M(G)) | (exp(G)) d , when exp(G) is odd, and exp(M(G)) | 2 d−1 (exp(G)) d , when exp(G) is even. Using our techniques, we obtain the following generalization of Theorem A of [25].…”

Section: (I) [Gh Gh Gh Gh H] = [H H H G H][h H G G H][h G H G H][g H ...mentioning

confidence: 99%

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On the Exponent of the Schur Multiplier

Antony,

Patali,

Thomas

2019

Preprint

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A longstanding problem attributed to I. Schur says that for a finite group G, the exponent of the second homology group H 2 (G, Z) divides the exponent of G. In this paper, we prove this conjecture for finite nilpotent groups of odd exponent and of nilpotency class 5, p-central metabelian p groups, and groups considered by L. E . Wilson in [30]. Moreover, we improve several bounds given by various authors.

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Section: (I) [Gh Gh Gh Gh H] = [H H H G H][h H G G H][h G H G H][g H ...mentioning

confidence: 59%

“…when exp(G) is even. Using our techniques, we obtain the following generalization of Theorem A of [25], which is one of their main results. Theorem 6.3.…”

Section: Introductionmentioning

confidence: 94%

Section: (I) [Gh Gh Gh Gh H] = [H H H G H][h H G G H][h G H G H][g H ...mentioning

confidence: 99%

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On the Exponent of the Schur Multiplier

Antony,

Patali,

Thomas

2019

Preprint

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“…Different variations and generalizations of representation groups have been studied, see e.g. [LT17,Sam15] for some of the most recent.…”

Section: The Yamazaki Covermentioning

confidence: 99%

Twisted group ring isomorphism problem

Margolis

Schnabel

2018

The Quarterly Journal of Mathematics

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Similarly to how the classical group ring isomorphism problem asks, for a commutative ring R, which information about a finite group G is encoded in the group ring RG, the twisted group ring isomorphism problem asks which information about G is encoded in all the twisted group rings of G over R.We investigate this problem over fields. We start with abelian groups and show how the results depend on the characteristic of R. In order to deal with non-abelian groups we construct a generalization of a Schur cover which exists also when R is not an algebraically closed field, but still linearizes all projective representations of a group. We then show that groups from the celebrated example of Everett Dade which have isomorphic group algebras over any field can be distinguished by their twisted group algebras over finite fields.

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“…In [15], Moravec prove that if G is a p-group of class c ≥ 2, then exp(M(G)) divides exp(G) 2⌊log 2 (c)⌋ . Later, in [1], Antony, Patali and Thomas proved that if p is odd, G is a finite p-group of nilpotency class c ≥ 2 and n = ⌈log 3 ( c+1 2 )⌉, then exp(M(G)) divides exp(G) n (see also [20] and the references given there). We obtain the following bound to exp(ν(G)), where G is an arbitrary p-group.…”

Section: Introductionmentioning

confidence: 99%

The exponent of the non-abelian tensor square and related constructions of $p$-groups

Bastos,

de Melo,

Gonçalves

et al. 2020

Preprint

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Let G be a group. We denote by ν(G) a certain extension of the non-abelian tensor square [G, G ϕ ] by G × G. In this paper we obtain bounds for the exponent of ν(G), when G is a finite p-group. In particular, we prove that if N is a potent normal subgroup of a G, then exp(ν(G)) divides p • exp(N ) • exp(ν(G/N )), where p denotes the prime p if p is odd and 4 if p = 2. As an application, we show that if G is a p-group of maximal class, then exp(ν(G)) divides p 2 • exp(G). We also establish a bound to exp(ν(G)) in terms of exp(G) and the coclass of G. Consequently, we improve some previous bounds to the exponent of Schur Multiplier M (G).

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The unitary cover of a finite group and the exponent of the Schur multiplier

Cited by 14 publications

References 17 publications

On the Exponent of the Schur Multiplier

On the Exponent of the Schur Multiplier

Twisted group ring isomorphism problem

The exponent of the non-abelian tensor square and related constructions of $p$-groups

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