Quotient Groups

1988 ◽  
pp. 79-85
Author(s):  
M. A. Armstrong
Keyword(s):  
Quotient Groups

Groups all proper quotient groups of which possess layer-Chernikov properties

1998 ◽  
Vol 50 (11) ◽  
pp. 1710-1718
Author(s):  
N. V. Kalashnikova
Keyword(s):  
Quotient Groups ◽  
Proper Quotient

Central quotient groups

1971 ◽  
Vol 10 (4) ◽  
pp. 679-684
Author(s):  
A. I. Moskalenko
Keyword(s):  
Central Quotient ◽  
Quotient Groups

Finite groups with all subgroups isomorphic to quotient groups

1973 ◽  
Vol 24 (1) ◽  
pp. 561-570 ◽  
Author(s):  
John H. Ying
Keyword(s):  
Finite Groups ◽  
Quotient Groups

Quotient groups and realization of tight Riesz groups

1973 ◽  
Vol 16 (4) ◽  
pp. 416-430 ◽  
Author(s):  
John Boris Miller
Keyword(s):  
Normal Subgroup ◽  
Open Interval ◽  
Canonical Homomorphism ◽  
Interval Topology ◽  
Essential Step ◽  
Image Position ◽  
Quotient Groups

Let (G, ≼) be an l-group having a compatible tight Riesz order ≦ with open-interval topology U, and H a normal subgroup. The first part of the paper concerns the question: Under what conditions on H is the structure of (G, ≼, ∧, ∨, ≦, U) carried over satisfactorily to by the canonical homomorphism; and its answer (Theorem 8°): H should be an l-ideal of (G, ≼) closed and not open in (G, U). Such a normal subgroup is here called a tangent. An essential step is to show that ≼′ is the associated order of ≦′.

scholarly journals Divisible quotient groups of reduced Abelian groups

1971 ◽  
Vol 1 (2) ◽  
pp. 353-356 ◽  
Author(s):  
Elbert A. Walker
Keyword(s):  
Abelian Groups ◽  
Quotient Groups

scholarly journals Sequential completeness of quotient groups

2000 ◽  
Vol 61 (1) ◽  
pp. 129-150 ◽  
Author(s):  
Dikran Dikranjan ◽  
Michael Tkačenko
Keyword(s):  
Abelian Group ◽  
Direct Products ◽  
Topological Groups ◽  
Complete Group ◽  
Sequential Completeness ◽  
Algebraic Properties ◽  
Countable Compactness ◽  
Quotient Groups

We discuss various generalisations of countable compactness for topological groups that are related to completeness. The sequentially complete groups form a class closed with respect to taking direct products and closed subgroups. Surprisingly, the stronger version of sequential completeness called sequential h-completeness (all continuous homomorphic images are sequentially complete) implies pseudocompactness in the presence of good algebraic properties such as nilpotency. We also study quotients of sequentially complete groups and find several classes of sequentially q-complete groups (all quotients are sequentially complete). Finally, we show that the pseudocompact sequentially complete groups are far from being sequentially q-complete in the following sense: every pseudocompact Abelian group is a quotient of a pseudocompact Abelian sequentially complete group.

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