Results 31 to 40 of about 72,032 (249)
A remark on elementary abelian groups [PDF]
Bulletin of the Australian Mathematical Society, 1977 Dr M.F. Newman has asked whether in the absence of the Axiom of Choice it is possible to have two non-isomorphic elementary abelian groups of the same (finite) exponent and of the same (infinite) cardinality. By means of an example, I show that this is in fact possible, if the exponent is at least five; I do not know the answer in the remaining two ...
openaire +2 more sources
On the structure of finite groups associated to regular non-centralizer graphs
AIMS Mathematics, 2023 The non-centralizer graph of a finite group $ G $ is the simple graph $ \Upsilon_G $ whose vertices are the elements of $ G $ with two vertices are adjacent if their centralizers are distinct.
Tariq A. Alraqad , Hicham Saber
doaj +1 more source
Elementary Properties of Ordered Abelian Groups [PDF]
Transactions of the American Mathematical Society, 1960 Introduction. A complete classification of abelian groups by their elementary properties (i.e. properties that can be formalized in the lower predicate calculus) was given by Szmielew [9]. No such attempt, however, has so far been made with respect to ordered groups.
Abraham Robinson, Elias Zakon
openaire +2 more sources
Elementary abelian groups of rank 5 are DCI-groups [PDF]
Journal of Combinatorial Theory, Series A, 2018 In this paper, we show that the group $\mathbb{Z}_p^5$ is a DCI-group for any odd prime $p,$ that is, two Cayley digraphs Cay$(\mathbb{Z}_p^5,S)$ and Cay$(\mathbb{Z}_p^5,T)$ are isomorphic if and only if $S=T^ $ for some automorphism $ $ of the group $\mathbb{Z}_p^5$.
Kovács, István, Feng, Yan-Quan
openaire +4 more sources
Elementary Extensions of Linear Topological Abelian Groups [PDF]
Proceedings of the American Mathematical Society, 1972 R. MacDowell and E. Specker obtain a structure theorem for elementary extensions of the integers by considering a certain residue mapping. In this paper we characterize those abelian groups in which an analogous situation exists and obtain the MacDowell-Specker result as a special case of our theory.
R. G. Phillips, P. L. Sperry
openaire +2 more sources
The Markov-Zariski topology of an abelian group [PDF]
, 2010 According to Markov, a subset of an abelian group G of the form {x in G: nx=a}, for some integer n and some element a of G, is an elementary algebraic set; finite unions of elementary algebraic sets are called algebraic sets. We prove that a subset of an
Dikranjan, Dikran, Shakhmatov, Dmitri
core +2 more sources
The torsion subgroup of the additive group of a Lie nilpotent associative ring of class 3 [PDF]
, 2013 Let $\mathbb Z \langle X \rangle$ be the free unital associative ring freely generated by an infinite countable set $X = \{ x_1,x_2, \dots \}$. Define a left-normed commutator $[x_1,x_2, \dots, x_n]$ by $[a,b] = ab - ba$, $[a,b,c] = [[a,b],c]$.
Deryabina, Galina, Krasilnikov, Alexei
core +1 more source
An approach to Quillen’s conjecture via centralisers of simple groups
Forum of Mathematics, Sigma, 2021 For any given subgroup H of a finite group G, the Quillen poset ${\mathcal {A}}_p(G)$ of nontrivial elementary abelian p-subgroups is obtained from ${\mathcal {A}}_p(H)$ by attaching elements via their centralisers in H.
Kevin Iván Piterman
doaj +1 more source
Modular invariants detecting the cohomology of BF_4 at the prime 3 [PDF]
, 2007 Attributed to J F Adams is the conjecture that, at odd primes, the mod-p cohomology ring of the classifying space of a connected compact Lie group is detected by its elementary abelian p-subgroups.
Broto, Carles
core +3 more sources
Sultan Qaboos University Journal for Science, 2009 The group of characters of an elementary Abelian group has been used to define duality between its subgroups, which in turn is extended to duality between group codes.
Adnan Abdulla Zain
doaj +1 more source