共查询到20条相似文献,搜索用时 0 毫秒
1.
Onofrio Mario Di Vincenzo Plamen Koshlukov Roberto La Scala 《Advances in Applied Mathematics》2006,37(4):541
In this paper we describe completely the involutions of the first kind of the algebra UTn(F) of n×n upper triangular matrices. Every such involution can be extended uniquely to an involution on the full matrix algebra. We describe the equivalence classes of involutions on the upper triangular matrices. There are two distinct classes for UTn(F) when n is even and a single class in the odd case.Furthermore we consider the algebra UT2(F) of the 2×2 upper triangular matrices over an infinite field F of characteristic different from 2. For every involution *, we describe the *-polynomial identities for this algebra. We exhibit bases of the corresponding ideals of identities with involution, and compute the Hilbert (or Poincaré) series and the codimension sequences of the respective relatively free algebras.Then we consider the *-polynomial identities for the algebra UT3(F) over a field of characteristic zero. We describe a finite generating set of the ideal of *-identities for this algebra. These generators are quite a few, and their degrees are relatively large. It seems to us that the problem of describing the *-identities for the algebra UTn(F) of the n×n upper triangular matrices may be much more complicated than in the case of ordinary polynomial identities. 相似文献
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Roksana Słowik 《Linear and Multilinear Algebra》2013,61(7):909-916
We describe involutions, i.e. elements of order 2, in the groups T n (K) – of upper triangular matrices of dimension n (n?∈??), and T ∞(K) – of upper triangular infinite matrices, where K is a field of characteristic different from 2. Using the obtained result, we give a formula for the number of all involutions in T n (K) in the case when K is a finite field. 相似文献
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Tobias Kildetoft 《代数通讯》2017,45(6):2325-2333
We define the position of an irreducible complex character of a finite group as an alternative to the degree. We then use this to define three classes of groups: position reducible (PR)-groups, inductively position reducible (IPR)-groups and weak IPR-groups. We show that IPR-groups and weak IPR-groups are solvable and satisfy the Taketa inequality (ie, that the derived length of the group is at most the number of degrees of irreducible complex characters of the group), and we show that any M-group is a weak IPR-group. We also show that even though PR-groups need not be solvable, they cannot be perfect. 相似文献
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Mahmut Kuzucuoğlu 《代数通讯》2013,41(10):3253-3262
The present article deals with locally finite groups G having an involution φ such that C G (φ) is an SF-group. It is shown that G possesses a normal subgroup B which is a central product of finitely many groups isomorphic to PSL(2, K i ) or SL(2, K i ) for some infinite locally finite fields K i of odd characteristic, such that [G, φ]′/B and G/[G, φ] are both SF-groups. 相似文献
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Yumiko Hironaka 《代数通讯》2017,45(8):3365-3376
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Alexander S. Kleshchev Pham Huu Tiep 《Transactions of the American Mathematical Society》2004,356(5):1971-1999
Let be an algebraically closed field of characteristic and be an almost simple group or a central extension of an almost simple group. An important problem in representation theory is to classify the subgroups of and -modules such that the restriction is irreducible. For example, this problem is a natural part of the program of describing maximal subgroups in finite classical groups. In this paper we investigate the case of the problem where is the Schur's double cover or .
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Marjeta Kramar 《Linear and Multilinear Algebra》2013,61(1):13-25
We describe the structure of irreducible matrix groups with submultiplicative spectrum. Since all such groups are nilpotent, the study is focused on p-groups. We obtain a block-monomial structure of matrices in irreducible p-groups and build polycyclic series arising from that structure. We give an upper bound to the exponent of these groups. We determine all minimal irreducible groups of p× p matrices with submultiplicative spectrum and discuss the case of p 2× p 2 matrices if p is an odd prime. 相似文献
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Daniil Shved 《代数通讯》2017,45(5):1842-1852
If G is an arbitrary group, then the group Autvt(G) consists, by definition, of all virtually trivial automorphisms of G, i.e. of all automorphisms that have the fixed-point subgroup of finite index in G. We investigate the structure of Autvt(G) and show that it possesses a certain “well-behaved” normal series which demonstrates its closeness to finitary linear groups. This is then used to prove that each simple section of Autvt(G) is a finitary linear group. 相似文献
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Marjeta Kramar 《Linear and Multilinear Algebra》2005,53(1):13-25
We describe the structure of irreducible matrix groups with submultiplicative spectrum. Since all such groups are nilpotent, the study is focused on p-groups. We obtain a block-monomial structure of matrices in irreducible p-groups and build polycyclic series arising from that structure. We give an upper bound to the exponent of these groups. We determine all minimal irreducible groups of p× p matrices with submultiplicative spectrum and discuss the case of p2× p2 matrices if p is an odd prime. 相似文献
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如果有限群G的每个子群与G的某个商群同构,则称群G为s-自对偶群.如果s-自对偶群G的每个商群与G的某个子群同构,则称群G为自对偶群.本文分类了每个真商群均为s-自对偶群的有限p-群.作为推论,本文还分类了每个真截段均为s-自对偶群的有限p-群,每个真商群均为自对偶群的有限p-群,以及每个真截段均为自对偶群的有限p-群... 相似文献
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Automorphisms of upper triangular matrix rings 总被引:2,自引:0,他引:2
S. Jøndrup 《Archiv der Mathematik》1987,49(6):497-502
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We show that there are characters of compact, connected, non-abelian groups that approximate random choices of signs. The work was motivated by Kronecker's theorem on the independence of exponential functions and has applications to thin sets.
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主要研究子群置换性质对有限群结构的影响.通过子群的置换性得到一类群,即B 群.B群是全可置换群的扩展,利用全可置换群的p次中心扩张和子群的阶得到B群的一些性质并对B 群的结构进行一些刻画.应用B 群的结构得到有限p (p〉2)群为二元生成的B 群的充要条件. 相似文献
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In this paper we investigate Jordan homomorphisms of upper triangular matrix rings and give a sufficient condition under which they are necessarily homomorphisms or anti-homomorphisms. 相似文献
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Jan Denef Franç ois Loeser 《Transactions of the American Mathematical Society》1998,350(12):5047-5066
The main result of this paper is a character sum identity for Coxeter arrangements over finite fields which is an analogue of Macdonald's conjecture proved by Opdam.
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Jordan isomorphisms of upper triangular matrix rings 总被引:1,自引:0,他引:1
Let R be a 2-torsionfree ring with identity 1 and let Tn(R), n ? 2, be the ring of all upper triangular n × n matrices over R. We describe additive Jordan isomorphisms of Tn(R) onto an arbitrary ring and generalize several results on this line. 相似文献