Infinite groups with a generalized dense system of subnormal subgroups

1982 ◽  
Vol 33 (3) ◽  
pp. 313-316
Author(s):  
L. A. Kurdachenko ◽  
N. F. Kuzennyi ◽  
V. V. Pylaev
Keyword(s):  
Infinite Groups ◽  
Dense System ◽  
Subnormal Subgroups

Some generalizations of normal series in infinite groups

1972 ◽  
Vol 14 (4) ◽  
pp. 496-502 ◽  
Author(s):  
Richard E. Phillips
Keyword(s):  
Finite Length ◽  
Infinite Groups ◽  
Normal Series ◽  
Group A ◽  
Complete Series ◽  
Image Position ◽  
Subnormal Subgroups

In this paper, we are concerned with certain generalizations of subnormal and ascendent (transfinitely subnormal) subgroups of a group. A subgroup A of a group G is called f-ascendent in G if there is a well ordered ascending complete series of subgroups of G, where for all α < λ, either Gα ⊲ Gα+1 or [Gα+1: Gα] < ∞. If such a series has finite length, A is called F-subnormal in G.

Subnormal structure in some classes of infinite groups

1973 ◽  
Vol 8 (1) ◽  
pp. 137-150 ◽  
Author(s):  
D.J. McCaughan
Keyword(s):  
Finite Group ◽  
Normal Subgroup ◽  
Intersection Property ◽  
Infinite Groups ◽  
Subnormal Structure ◽  
Torsion Free ◽  
Subnormal Subgroups

Let p be a prime and G a group with a p–reduced nilpotent normal subgroup N such that G/N is a nilpotent p–group. It is shown that if G has the subnormal intersection property and if G/N is finite or N is p–torsion-free, then G is nilpotent. This result is used to prove that an abelian-by-finite group has the subnormal intersection property if and only if it has a bound for the subnormal indices of its subnormal subgroups.

scholarly journals Semigroups with few endomorphisms

1969 ◽  
Vol 10 (1-2) ◽  
pp. 162-168 ◽  
Author(s):  
Vlastimil Dlab ◽  
B. H. Neumann
Keyword(s):  
Cyclic Group ◽  
Finite Groups ◽  
Automorphism Groups ◽  
Infinite Groups ◽  
Infinite Cyclic Group

Large finite groups have large automorphism groups [4]; infinite groups may, like the infinite cyclic group, have finite automorphism groups, but their endomorphism semigroups are infinite (see Baer [1, p. 530] or [2, p. 68]). We show in this paper that the corresponding propositions for semigroups are false.

Cardinal invariants of infinite groups

1990 ◽  
Vol 30 (3) ◽  
pp. 155-170
Author(s):  
Jörg Brendle
Keyword(s):  
Infinite Groups ◽  
Cardinal Invariants

scholarly journals On perfect subnormal subgroups of finite groups

1975 ◽  
Vol 36 (2) ◽  
pp. 242-251 ◽  
Author(s):  
John S Wilson
Keyword(s):  
Finite Groups ◽  
Subnormal Subgroups

Some Remarks on Infinite Groups

1937 ◽  
Vol s1-12 (2) ◽  
pp. 120-127 ◽  
Author(s):  
B. H. Neumann
Keyword(s):  
Infinite Groups
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