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Invariant Brauer group of an abelian variety
Israel Journal of Mathematics, 2020We study a new object that can be attached to an abelian variety or a complex torus: the invariant Brauer group, as recently defined by Yang Cao. Over the field of complex numbers this is an elementary abelian 2-group with an explicit upper bound on the ...
M. Orr +3 more
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Interlacing of elementary abelian groups
Mathematical Notes of the Academy of Sciences of the USSR, 1972A lattice of characteristic subgroups of multiple interlacings of finite elementary abelian groups by itself is established herein.
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The multiplier conjecture for elementary abelian groups
Journal of Combinatorial Designs, 1994AbstractApplying the method that we presented in [19], in this article we prove: “Let G be an elementary abelian p‐group. Let n = dn1. If d(≠ p) is a prime not dividing n1, and the order w of d mod p satisfies \documentclass{article}\pagestyle{empty}\begin{document}$ w > \frac{{d^2}}{3} $\end{document}, then the Second Multiplier Theorem holds ...
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1992
Elementary abelian groups can be thought of as additive groups of finite fields. As such, all of the tools of field theory are available to us in the study of orthomorphism graphs of these groups. In particular, any function from a finite field to itself, and thus any orthomorphism of the additive group of the field, can be realized as a polynomial ...
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Elementary abelian groups can be thought of as additive groups of finite fields. As such, all of the tools of field theory are available to us in the study of orthomorphism graphs of these groups. In particular, any function from a finite field to itself, and thus any orthomorphism of the additive group of the field, can be realized as a polynomial ...
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Groups with elementary Abelian centralizers of involutions
Algebra and Logic, 2007An involution i of a group G is said to be almost perfect in G if any two involutions of iG the order of a product of which is infinite are conjugated via a suitable involution in iG. We generalize a known result by Brauer, Suzuki, and Wall concerning the structure of finite groups with elementary Abelian centralizers of involutions to groups with ...
A. S. Kryukovskii, A. I. Sozutov
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On groups admitting an elementary Abelian automorphism group
1974Recently a number of theorems have been proved showing that if V is a fixedpoint-free group of automorphisms of the finite group G then, with certain additional assumptions, G is soluble. These theorems may be found in [3], [4], [6] and [7].
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Elementary abelian groups acting on products of spheres
Mathematische Zeitschrift, 1998A classical result in transformation groups says a finite abelian group acting freely on a sphere must be cyclic. This result was extended by G. Carlsson. If \(G\) is an elementary abelian \(p\) group of rank \(r\), and \(G\) acts freely, cellularly, and homologically trivially on a CW-complex \(X\simeq(S^n)^k\), then \(k\geq r\).
David J. Benson, Alejandro Adem
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Elementary Abelian Cartesian Groups Cartesian Groups
Canadian Journal of Mathematics, 1988Throughout the paper, G will denote an additively written, but not always abelian, group of finite order n; and X = (xij) will denote a square matrix of order n with entries from G and whose rows and columns are numbered 0, 1, …, n − 1. We call X a cartesian array (afforded by G) if(1.1) The sequence {−xmi + xki, i = 0,…, n – 1} contains all elements ...
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Elementary equivalence for abelian-by-finite and nilpotent groups
Journal of Symbolic Logic, 2001AbstractWe show that two abelian-by-finite groups are elementarily equivalent if and only if they satisfy the same sentences with two alternations of quantifiers. We also prove that abelian-by-finite groups satisfy a quantifier elimination property. On the other hand, for each integer n, we give some examples of nilpotent groups which satisfy the same ...
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An addition theorem for the elementary Abelian group of type (p, p)
, 1986H. B. Mann, Ying Fou Wou
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