Results 1 to 10 of about 176,865 (291)
An Elementary Abelian Group of Rank 4 Is a CI-Group
Journal of Combinatorial Theory, Series A, 2001 Finite groups are dealt with. In addition to the known notion of CI-group (i.e., group possessing the Cayley isomorphism property), the authors consider the related concept of \(\text{CI}^{(2)}\)-group. Let \(F\), \(G\) be subgroups of the symmetric (permutation) group \(\text{Sym}(X)\). We say that \(G(\supseteq F)\) is \(F\)-transjugate if \(G\) acts
Mitsugu Hirasaka, Mikhail Muzychuk
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An elementary abelian group of large rank is not a CI-group
Discrete Mathematics, 2003 We say that a finite group \(H\) has the Cayley isomorphy (CI) property (or, shortly, \(H\) is a CI-group) if any pair of directed Cayley graphs over \(H\) is non-isomorphic unless an isomorphism exists between the digraphs which can be induced by an automorphism of \(H\).
Mikhail Muzychuk
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An addition theorem for the elementary abelian group
Journal of Combinatorial Theory, 1968 Summary: Let \(S(a_1,\ldots, a_s)\) be the set of all sums over subsequences of a sequence \(\{a_1,\ldots, a_s\}\), \(a_1\neq 0\), from an abelian group \(G\). The author proves: If \(G\) is an abelian group of order \(p^n\) \((n\geq 2)\) then: (i) If \(s\geq 2^{n-1}(p-1)\) then \(S(a_1,\ldots, a_s)\) includes a coset of a subgroup of order \(p\). (ii)
John E. Olson
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On Group Codes Over Elementary Abelian Groups [PDF]
Sultan Qaboos University Journal for Science, 2003 For group codes over elementary Abelian groups we present definitions of the generator and the parity check matrices, which are matrices over the ring of endomorphism of the group.
Adnan A. Zain
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Elementary Abelian 2-subgroups in an Autotopism Group of a Semifield Projective Plane
Известия Иркутского государственного университета: Серия "Математика", 2020 Elementary Abelian 2-subgroups in an Autotopism Group of a Semifield Projective Plane} We investigate the hypotheses on a solvability of the full collineation group for non-Desarguesian semifield projective plane of a finite order (the question 11.76 in ...
O. V. Kravtsova
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Varieties for Modules of Quantum Elementary Abelian Groups [PDF]
Algebras and Representation Theory, 2008 We define a rank variety for a module of a noncocommutative Hopf algebra $A = \rtimes G$ where $ = k[X_1, ..., X_m]/(X_1^{\ell}, ..., X_m^{\ell})$, $G = ({\mathbb Z}/\ell{\mathbb Z})^m$, and $\text{char} k$ does not divide $\ell$, in terms of certain subalgebras of $A$ playing the role of "cyclic shifted subgroups".
Julia Pevtsova, Sarah Witherspoon
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Electronic Journal of Combinatorics, 2018 We show that if certain arithmetic conditions hold, then the Cayley isomorphism problem for abelian groups, all of whose Sylow subgroups are elementary abelian or cyclic, reduces to the Cayley isomorphism problem for its Sylow subgroups.
Ted Dobson
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On Elementary Abelian Cartesian Groups [PDF]
Canadian Mathematical Bulletin, 1991 AbstractJ. Hayden [2] proved that, if a finite abelian group is a Cartesian group satisfying a certain "homogeneity condition", then it must be an elementary abelian group. His proof required the character theory of finite abelian groups. In this note we present a shorter, elementary proof of his result.
Anthony B. Evans
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Separating invariants for certain representations of the elementary Abelian p-groups of rank two
AIMS MathematicsFor a finite group acting linearly on a vector space, a separating set is a subset of the invariant ring that separates the orbits. In this paper, we determined explicit separating sets in the corresponding rings of invariants for four families of finite
Panpan Jia , Jizhu Nan, Yongsheng Ma
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Varieties and elementary Abelian groups
Journal of Pure and Applied Algebra, 1982 J. L. Alperin, Leonard Evens
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