共查询到20条相似文献，搜索用时 15 毫秒
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In this paper we study properties of the partial Schur multiplier. As an application a characterization of components of the partial Schur multiplier for some groups is given. We also describe the classical Schur multiplier of elementary abelian 2-groups by using partial factor sets. 相似文献
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《Journal of Pure and Applied Algebra》2024,228(1):107463
In 1956, Green provided a bound on the order of the Schur multiplier of p-groups. This bound, given as a function of the order of the group, is the best possible. Since then, the bound has been refined numerous times by adding other inputs to the function, such as, the minimal number of generators of the group and the order of the derived subgroup. We strengthen these bounds by adding another input, the group's nilpotency class. The specific cases of nilpotency class 2 and maximal class are discussed in greater detail. 相似文献
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R. J. Higgs 《代数通讯》2013,41(11):4224-4233
In this article we will study the restriction of the irreducible projective characters of a finite group to a central subgroup. We will also consider under what conditions on the restriction of such irreducible projective characters to an abelian normal subgroup that we can deduce that the subgroup is central. Finally, we will investigate the relationship between the inertia subgroup and the absolute centralizer of a central subgroup relative to a fixed 2-cocycle of the group. 相似文献
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In this article, we classify up to isomorphism the character tables of 2-generator p-groups of class two. 相似文献
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In Ok (2001), the structure of the Schur multiplier was found for six of the ten non-Abelian groups of order p 4, for p an odd prime number. In this article, using elementary methods, we will establish the structure of the Schur multiplier for the remaining four groups. This subject has only received cursory attention previously and a number of small errors have been made in the existing literature. However, the main result of this article will be to find the projective character degree patterns with multiplicities and the epicentres of all p-groups of order p 4. 相似文献
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Shigeharu Takayama 《Transactions of the American Mathematical Society》2003,355(1):37-47
We give a new characterization of Iitaka's fibration of algebraic varieties associated to line bundles. Introducing an ``intersection number' of line bundles and curves by using the notion of multiplier ideal sheaves, Iitaka's fibration can be regarded as a ``numerically trivial fibration' in terms of this intersection theory.
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William D. Banks Asma Harcharras 《Proceedings of the American Mathematical Society》2004,132(7):2121-2125
We show that if the norm of an idempotent Schur multiplier on the Schatten class lies sufficiently close to , then it is necessarily equal to . We also give a simple characterization of those idempotent Schur multipliers on whose norm is .
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Pradeep K. Rai 《代数通讯》2013,41(10):3982-3986
We give a bound on the dimension of the Schur multiplier of a finite dimensional nilpotent Lie algebra which sharpens the earlier known bounds. 相似文献
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S. W. Drury 《Linear algebra and its applications》1998,280(2-3):217-227
In this article we show how to estimate the trace multiplier norm of a rank 2 matrix. As an application, an alternative proof of a theorem of Holbrook et al. (Maximal spectral distance, Linear Algebra Appl., 249 (1996) 197–205) on the maximal spectral distance between two normal matrices with prescribed eigenvalues is given. 相似文献
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In this article, some inequalities of the dimension of Schur multiplier of pairs of Lie algebras will be obtained and new upper bound will be compared with the existing ones in the literature. Furthermore, by using homological methods, we will derive some properties of the higher Schur multiplier of a pair of Lie algebras and give some isomorphisms that generalize some known results of Stallings in group theory setting. 相似文献
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Peyman Niroomand 《Linear and Multilinear Algebra》2013,61(8):831-836
For every finite p-group G of order p n with derived subgroup of order p m , Rocco [N.R. Rocco, On a construction related to the nonabelian tensor square of a group, Bol. Soc. Brasil. Mat. 1 (1991), pp. 63–79] proved that the order of tensor square of G is at most p n(n?m). This upper bound has been improved recently by the author [P. Niroomand, On the order of tensor square of non abelian prime power groups (submitted)]. The aim of this article is to obtain a similar result for a non-abelian nilpotent Lie algebra of finite dimension. More precisely, for any given n-dimensional non-abelian nilpotent Lie algebra L with derived subalgebra of dimension m we have dim(L???L)?≤?(n???m)(n???1)?+?2. Furthermore for m?=?1, the explicit structure of L is given when the equality holds. 相似文献
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Let (H, N) be a pair of finite p-groups, in which N is a normal subgroup of H. In the present article, some upper bounds for the order of the commutator subgroup [N, H] are given. It is also constructed an upper bound for the order of the Schur multiplier of the pair of finite p-groups. 相似文献
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The purpose of this note is to define a graph whose vertex set is a finite group
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Maurizio Monge 《Discrete Applied Mathematics》2011,159(11):1176-1179
Consider the set of vectors over a field having non-zero coefficients only in a fixed sparse set and multiplication defined by convolution, or the set of integers having non-zero digits (in some base b) in a fixed sparse set. We show the existence of an optimal (or almost-optimal, in the latter case) ‘magic’ multiplier constant that provides a perfect hash function which transfers the information from the given sparse coefficients into consecutive digits. Studying the convolution case we also obtain a result of non-degeneracy for Schur functions as polynomials in the elementary symmetric functions in positive characteristic. 相似文献