Results 1 to 10 of about 235,315 (244)
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 p-groups of rank 2p+3 are not CI-groups [PDF]
arXiv, 2009 For every prime $p > 2$ we exhibit a Cayley graph of $\mathbb{Z}_p^{2p+3}$ which is not a CI-graph. This proves that an elementary Abelian $p$-group of rank greater than or equal to $2p+3$ is not a CI-group. The proof is elementary and uses only multivariate polynomials and basic tools of linear algebra.
Gábor Somlai
arxiv +3 more sources
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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A characterisation of elementary abelian 3-groups [PDF]
arXiv, 2016 Tarnauceanu [Archiv der Mathematik, 102 (1), (2014), 11--14] gave a characterisation of elementary abelian $2$-groups in terms of their maximal sum-free sets. His theorem states that a finite group $G$ is an elementary abelian $2$-group if and only if the set of maximal sum-free sets coincides with the set of complements of the maximal subgroups.
arxiv +4 more sources
Commuting involutions and elementary abelian subgroups of simple groups [PDF]
arXiv, 2020 Motivated in part by representation theoretic questions, we prove that if G is a finite quasi-simple group, then there exists an elementary abelian subgroup of G that intersects every conjugacy class of involutions of G.
Robert M. Guralnick +1 more
arxiv +3 more sources
An Elementary Abelian Group of Rank 4 Is a CI-Group
Journal of Combinatorial Theory, Series A, 2001 AbstractIn this paper we prove that Z4p is a CI-group; i.e., two Cayley graphs over the elementary abelian group Z4p are isomorphic if and only if their connecting sets are conjugate by an automorphism of the group Z4p.
Mitsugu Hirasaka, Mikhail Muzychuk
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An elementary abelian group of large rank is not a CI-group
Discrete Mathematics, 2003 AbstractIn this paper, we prove that the group Zpn is not a CI-group if n⩾2p−1+(2p−1p), that is there exist two Cayley digraphs over Zpn which are isomorphic but their connection sets are not conjugate by an automorphism of Zpn.
Mikhail Muzychuk
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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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An addition theorem for the elementary abelian group
Journal of Combinatorial Theory, 1968 AbstractIn this paper we investigate the set of all sums over subsequences of a sequence a1,…, as of elements in a finite elementary Abelian group.
John E. Olson
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