scholarly journals A NORMAL NON-CAYLEY-INVARIANT GRAPH FOR THE ELEMENTARY ABELIAN GROUP OF ORDER 64

2008 ◽  
Vol 85 (03) ◽  
pp. 347 ◽  
Author(s):  
GORDON F. ROYLE
Keyword(s):  
Abelian Group ◽  
Elementary Abelian Group ◽  
Invariant Graph

Functors on Finite Vector Spaces and Units in Abelian Group Rings

1986 ◽  
Vol 29 (1) ◽  
pp. 79-83 ◽  
Author(s):  
Klaus Hoechsmann
Keyword(s):  
Abelian Group ◽  
Group Ring ◽  
Elementary Abelian Group ◽  
Vector Spaces ◽  
Group Rings ◽  
Cyclic Subgroups ◽  
Group Of Units ◽  
Finite Vector ◽  
Finite Vector Spaces

AbstractIf A is an elementary abelian group, let (A) denote the group of units, modulo torsion, of the group ring Z[A]. We study (A) by means of the compositewhere C and B run over all cyclic subgroups and factor-groups, respectively. This map, γ, is known to be injective; its index, too, is known. In this paper, we determine the rank of γ tensored (over Z);with various fields. Our main result depends only on the functoriality of

scholarly journals The Noether number of p-groups

2019 ◽  
Vol 18 (04) ◽  
pp. 1950066 ◽  
Author(s):  
Kálmán Cziszter
Keyword(s):  
Abelian Group ◽  
Heisenberg Group ◽  
Cyclic Subgroup ◽  
Elementary Abelian Group ◽  
Polynomial Invariant

A group of order [Formula: see text] ([Formula: see text] prime) has an indecomposable polynomial invariant of degree at least [Formula: see text] if and only if the group has a cyclic subgroup of index at most [Formula: see text] or it is isomorphic to the elementary abelian group of order 8 or the Heisenberg group of order 27.

scholarly journals DERIVED SUBGROUPS OF FIXED POINTS IN PROFINITE GROUPS

2011 ◽  
Vol 54 (1) ◽  
pp. 97-105
Author(s):  
CRISTINA ACCIARRI ◽  
ALINE DE SOUZA LIMA ◽  
PAVEL SHUMYATSKY
Keyword(s):  
Abelian Group ◽  
Fixed Points ◽  
Profinite Group ◽  
Elementary Abelian Group ◽  
Profinite Groups ◽  
Locally Finite ◽  
Group Of Automorphisms

AbstractThe main result of this paper is the following theorem. Let q be a prime and A be an elementary abelian group of order q3. Suppose that A acts as a coprime group of automorphisms on a profinite group G in such a manner that CG(a)′ is periodic for each a ∈ A#. Then G′ is locally finite.

scholarly journals Elementary abelian operator groups and admissible formations

1983 ◽  
Vol 34 (1) ◽  
pp. 71-91
Author(s):  
Fletcher Gross
Keyword(s):  
Abelian Group ◽  
Elementary Abelian Group ◽  
Identity Elements

AbstractSuppose the elementary abelian group A acts on the group G where A and G have relatively prime orders. If CG(a) belongs to some formation F for all non-identity elements a in A, does it follow that G belongs to F? For many formations, the answer is shown to be yes provided that the rank of A is sufficiently large.

The non-solvable doubly transitive dimensional dual hyperovals

2018 ◽  
Vol 18 (1) ◽  
pp. 1-4
Author(s):  
Ulrich Dempwolff
Keyword(s):  
Abelian Group ◽  
Automorphism Group ◽  
Elementary Abelian Group ◽  
Dual Hyperoval ◽  
Dimensional Dual Hyperovals

AbstractIn [9] S. Yoshiara determines possible automorphism group of doubly transitive dimensional dual hyperovals. He shows that a doubly transitive dual hyperovalDis either isomorphic to the Mathieu dual hyperoval or the dual hyperoval is defined over 𝔽2, and if the hyperoval has rankn, the automorphism group has the formE⋅S, with an elementary abelian groupEof order 2nandSa subgroup of GL(n,2) acting transitively on the nontrivial elements ofE. Moreover Yoshiara describes the possible candidates forS. In this paper we assume thatSis non-solvable and show that then the dimensional dual hyperoval is a bilinear quotient of a Hyubrechts dual hyperoval.

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