منابع مشابه
Finite groups have even more centralizers
For a finite group $G$, let $Cent(G)$ denote the set of centralizers of single elements of $G$. In this note we prove that if $|G|leq frac{3}{2}|Cent(G)|$ and $G$ is 2-nilpotent, then $Gcong S_3, D_{10}$ or $S_3times S_3$. This result gives a partial and positive answer to a conjecture raised by A. R. Ashrafi [On finite groups with a given number of centralizers, Algebra Collo...
متن کاملfinite groups have even more centralizers
for a finite group $g$, let $cent(g)$ denote the set of centralizers of single elements of $g$. in this note we prove that if $|g|leq frac{3}{2}|cent(g)|$ and $g$ is 2-nilpotent, then $gcong s_3, d_{10}$ or $s_3times s_3$. this result gives a partial and positive answer to a conjecture raised by a. r. ashrafi [on finite groups with a given number of centralizers, algebra collo...
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This paper is devoted to the study of lattices generated by finite Abelian groups. Special species of such lattices arise in the exploration of elliptic curves over finite fields. In the case where the generating group is cyclic, they are also known as the Barnes lattices. It is shown that for every finite Abelian group with the exception of the cyclic group of order four these lattices have a ...
متن کاملFinite Linear Groups, Lattices, and Products of Elliptic Curves
Let V be a finite dimensional complex linear space and let G be an irreducible finite subgroup of GL(V ). For a G-invariant lattice Λ in V of maximal rank, we give a description of structure of the complex torus V/Λ. In particular, we prove that for a wide class of groups, V/Λ is isogenous to a self-product of an elliptic curve, and that in many cases V/Λ is isomorphic to a product of mutually ...
متن کاملCrystallographic and Quasicrystallographic Lattices from the Finite Groups of Quaternions
Quaternions are ordered quadruples of four numbers subject to specified rules of addition and multiplication, which can represent points in four-dimensional (4D) space and which form finite groups under multiplication isomorphic to polyhedral groups. Projection of the 8 quaternions of the dihedral group D2h, with only two-fold symmetry, into 3D space provides a basis for crystal lattices up to ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1976
ISSN: 0021-8693
DOI: 10.1016/0021-8693(76)90234-9