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We characterize the group algebras of finite groups over a field of characteristic 2 with metabelian groups of units.Dedicated to Professor László Fuchs on his 70th birthdayResearch was supported by Hungarian National Fund for Scientific Research grant No. T014279  相似文献   

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We classify the quadratic extensions and the finite groups G for which the group ring [G] of G over the ring of integers of K has the property that the group of units of augmentation 1 is hyperbolic. We also construct units in the ℤ-order of the quaternion algebra , when it is a division algebra.  相似文献   

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Let FG be a group algebra of a group G over a field F and U (FG) the unit group of FG. It is a classical question to determine the structure of the unit group of the group algebra of a finite group over a finite field. In this article, the structure of the unit group of the group algebra of the non-abelian group G with order 21 over any finite field of characteristic 3 is established. We also characterize the structure of the unit group of FA 4 over any finite field of characteristic 3 and the structure of the unit group of FQ 12 over any finite field of characteristic 2, where Q 12 = 〈x, y; x 6 = 1, y 2 = x 3, x y = x ?1〉.  相似文献   

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Ram and Rammage have introduced an automorphism and Clifford theory on affine Hecke algebras. Here we will extend them to cyclotomic Hecke algebras and rational Cherednik algebras.  相似文献   

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Two groups with isomorphic group algebras   总被引:1,自引:0,他引:1  
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The purpose of this paper is to show the vastness of the class of generalized strongly monomial groups and the implication of its study on monomiality questions studied by group theorists. The so called generalized strongly monomial groups, which is a generalization of strongly monomial groups introduced by Olivieri, del Río and Simón, arose in a recent work of authors while understanding the algebraic structure of rational group algebras.  相似文献   

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LetF be a field of characteristicp>0 and letG be an arbitrary abelian group written multiplicatively withp-basis subgroup denoted byB. The first main result of the present paper is thatB is an isomorphism invariant of theF-group algebraFG. In particular, thep-local algebraically compact groupG can be retrieved fromFG. Moreover, for the lower basis subgroupB 1 of thep-componentG p it is shown thatG p/Bl is determined byFG. Besides, ifH is (p-)high inG, thenG p/Hp andH p n[p] for ℕ0 are structure invariants forFG, andH[p] as a valued vector space is a structural invariant forN 0 G, whereN p is the simple field ofp-elements. Next, presume thatG isp-mixed with maximal divisible subgroupD. ThenD andF(G/D) are functional invariants forFG. The final major result is that the relative Ulm-Kaplansky-Mackeyp-invariants ofG with respect to the subgroupC are isomorphic invariants of the pair (FG, FC) ofF-algebras. These facts generalize and extend analogous in this aspect results due to May (1969), Berman-Mollov (1969) and Beers-Richman-Walker (1983). As a finish, some other invariants for commutative group algebras are obtained.  相似文献   

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Paul Hill  William Ullery 《代数通讯》2013,41(12):4029-4038
Suppose F is a perfect field of characteristic p 0 and G is an abelian group whose torsion subgroup Gt is p-primary. If Gt is totally projective of countable length, it is shown that G is a direct factor of the group of normalized units V(G) of the group algebra F(G) and that V(G)/G is a totally projective p-group. The proof of this result is based on a new characterization of the class of totally projective p-groups of countable length. Li addition, the same result regarding V(G) is obtained if G has countable torsion-free rank and Gt is totally projective of length less than ω1 + ω0 . Finally, these results are applied to the question of whether the existence of an F-i pomorphism F(G) ? F(H) for some group H implies that G?H.  相似文献   

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Let k ≧ 3 be an integer or k = ∞ and let K be a field. There is a recursive family of finitely presented groups Gn over a fixed finite alphabet with solvable word problem such that
(1)  the center of Gn is trivial for every
(2)  the dimension d(n) of the center of the group algebra K · Gn over K is either 1 or k, and
(3)  it is undecidable given n whether d(n) = 1 or d(n) = k.
Received: 22 July 2004  相似文献   

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We give a result on Cartan invariants of the group algebra of a finite group over an algebraically closed field , which implies that if the Loewy length (socle length) of the projective indecomposable -module corresponding to the trivial -module is four, then has characteristic 2. The proof is independent of the classification of finite simple groups.

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Let G be a compactly generated group of polynomial growth and a weight function on G. For a large class of weights we characterize symmetry of the weighted group algebra L 1 (G,). In particular, if the weight is sub-exponential, then the algebra L 1 (G,) is symmetric. For these weights we develop a functional calculus on a total part of L 1 (G,) and use it to prove the Wiener property. Mathematics Subject Classification (2000):43A20, 22D15, 22D12.Supported by the Austrian Science Foundation project FWF P-14485.Supported by the research grants MEN/CUL/98/007 and CUL/01/014.  相似文献   

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