Necessary conditions for the coperiodicity of quotients of direct products of Abelian groups

1984 ◽  
Vol 35 (6) ◽  
pp. 484-487
Author(s):  
A. M. Ivanov
Keyword(s):  
Necessary Conditions ◽  
Abelian Groups ◽  
Direct Products

COMMUTING PROPERTIES OF EXT

2013 ◽  
Vol 94 (2) ◽  
pp. 276-288 ◽  
Author(s):  
PHILL SCHULTZ
Keyword(s):  
Abelian Groups ◽  
Direct Products ◽  
Direct Sums

AbstractWe characterize the abelian groups $G$ for which the functors $\mathrm{Ext} (G, - )$ or $\mathrm{Ext} (- , G)$ commute with or invert certain direct sums or direct products.

scholarly journals On lacunary sets for nonabelian groups

1978 ◽  
Vol 25 (2) ◽  
pp. 167-176 ◽  
Author(s):  
A. H. Dooley
Keyword(s):  
Necessary Conditions ◽  
Abelian Groups ◽  
Sidon Sets ◽  
Compact Abelian Groups ◽  
Nonabelian Groups

AbstractResults concerning a class of lacunary sets are generalized from compact abelian to compact nonabelian groups. This class was introduced for compact abelian groups by Bozejko and Pytlik; it includes the p-Sidon sets of Edwards and Ross. A notion of test family is introduced and is used to give necessary conditions for a set to be lacunary. Using this, it is shown that (2) has no infinite p-Sidon sets for 1 ≤p<2.

Theories of modules closed under direct products

1992 ◽  
Vol 57 (2) ◽  
pp. 515-521
Author(s):  
Roger Villemaire
Keyword(s):  
Direct Product ◽  
Abelian Groups ◽  
Complete Theory ◽  
Direct Products ◽  
Horn Theory

AbstractWe generalize to theories of modules (complete or not) a result of U. Felgner stating that a complete theory of abelian groups is a Horn theory if and only if it is closed under products. To prove this we show that a reduced product of modules ΠFMi (i ϵ I) is elementarily equivalent to a direct product of ultraproducts of the modules Mi(i ϵ I).

scholarly journals Subalgebras, direct products and associated lattices of MV-algebras

1992 ◽  
Vol 34 (3) ◽  
pp. 301-307 ◽  
Author(s):  
L. P. Belluce ◽  
A. Di Nola ◽  
A. Lettieri
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Propositional Logic ◽  
Abelian Groups ◽  
Completeness Theorem ◽  
Direct Products ◽  
Algebraic Proof ◽  
Mv Algebras

MV-algebras were introduced by C. C. Chang [3] in 1958 in order to provide an algebraic proof for the completeness theorem of the Lukasiewicz infinite valued propositional logic. In recent years the scope of applications of MV-algebras has been extended to lattice-ordered abelian groups, AF C*-algebras [10] and fuzzy set theory [1].

Semicomplete Finite p-Groups

2011 ◽  
Vol 18 (spec01) ◽  
pp. 937-944 ◽  
Author(s):  
M. Shabani Attar
Keyword(s):  
Automorphism Group ◽  
Commutator Subgroup ◽  
Necessary Conditions ◽  
Abelian Groups ◽  
Inner Automorphism

Let G be a group and G' be its commutator subgroup. An automorphism α of G is called an IA-automorphism if x-1α (x) ∈ G' for each x ∈ G. The set of all IA-automorphisms of G is denoted by IA (G). A group G is called semicomplete if and only if IA (G)= Inn (G), where Inn (G) is the inner automorphism group of G. In this paper we characterize semicomplete finite p-groups of class 2, give some necessary conditions for finite p-groups to be semicomplete, and characterize semicomplete non-abelian groups of orders p4 and p5.

scholarly journals Radical Classes Closed Under Products

2013 ◽  
Vol 21 (3) ◽  
pp. 103-132
Author(s):  
Barry Gardner
Keyword(s):  
Abelian Groups ◽  
Direct Products ◽  
Radical Theory ◽  
Associative Rings ◽  
Regular Rings

Abstract This is a survey of what is known about Kurosh-Amitsur radical classes which are closed under direct products. Associative rings, groups, abelian groups, abelian ℓ-groups and modules are treated. We have attempted to account for all published results relevant to this topic. Many or most of these were not, as published, expressed in radical theoretic terms, but have consequences for radical theory which we point out. A fruitful source of results and examples is the notion of slenderness for abelian groups together with its several variants for other structures. We also present a few new results, including examples and a demonstration that e-varieties of regular rings are product closed radical classes of associative rings.

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