Groups with Finitely Many Homomorphic Images of Finite Rank

2016 ◽  
Vol 23 (02) ◽  
pp. 181-187
Author(s):  
Francesco de Giovanni ◽  
Alessio Russo
Keyword(s):  
Large Class ◽  
Finite Rank ◽  
Minimal Condition ◽  
Soluble Groups ◽  
Normal Series ◽  
Černikov Group

A group is called a Černikov group if it is abelian-by-finite and satisfies the minimal condition on subgroups. A new characterization of Černikov groups is given here, by proving that in a suitable large class of generalised soluble groups they coincide with the groups having only finitely many homomorphic images of finite rank (up to isomorphisms) and admitting an ascending normal series whose factors have finite rank.

Normal series of soluble groups of finite rank

1986 ◽  
Vol 46 (4) ◽  
pp. 289-298
Author(s):  
J. F. Bowers
Keyword(s):  
Finite Rank ◽  
Soluble Groups ◽  
Normal Series

A NOTE ON SOLUBLE GROUPS WITH THE MINIMAL CONDITION ON NORMAL SUBGROUPS

2014 ◽  
Vol 13 (04) ◽  
pp. 1350134 ◽  
Author(s):  
M. DE FALCO ◽  
F. DE GIOVANNI ◽  
C. MUSELLA
Keyword(s):  
Finite Rank ◽  
Soluble Group ◽  
Minimal Condition ◽  
Normal Subgroups ◽  
Soluble Groups ◽  
Infinite Rank

It is known that there exist soluble groups of infinite rank which satisfy the minimal condition on normal subgroups. We prove here that if G is any soluble group satisfying the minimal condition on normal subgroups of infinite rank, then either G has finite rank or it satisfies the minimal condition on normal subgroups.

Some inequalities for moments and coefficients of variation for a large class of probability functions

1979 ◽  
Vol 16 (3) ◽  
pp. 665-670 ◽  
Author(s):  
Burt V. Bronk
Keyword(s):  
Large Class ◽  
Average Molecular Weight ◽  
Empirical Measure ◽  
Number Average Molecular Weight ◽  
Positive Real ◽  
Coefficients Of Variation ◽  
Probability Densities ◽  
Rigorous Bounds ◽  
Illustrative Application

Some inequalities for moments and coefficients of variation of probability densities over the positive real line are obtained by means of simple geometrical relationships. As an illustrative application rigorous bounds are obtained for the ratio of weight average to number average molecular weight for a large class of distributions of macromolecules, giving a more precise characterization of this empirical measure of heterogeneity.

Central automorphisms of free nilpotent Lie algebras

2017 ◽  
Vol 16 (11) ◽  
pp. 1750205
Author(s):  
Özge Öztekin ◽  
Naime Ekici
Keyword(s):  
Lie Algebras ◽  
Finite Rank ◽  
Characteristic Zero ◽  
Sufficient Conditions ◽  
Nilpotency Class ◽  
Nilpotent Lie Algebra ◽  
Central Automorphism ◽  
Nilpotent Lie Algebras ◽  
Central Automorphisms

Let [Formula: see text] be the free nilpotent Lie algebra of finite rank [Formula: see text] [Formula: see text] and nilpotency class [Formula: see text] over a field of characteristic zero. We give a characterization of central automorphisms of [Formula: see text] and we find sufficient conditions for an automorphism of [Formula: see text] to be a central automorphism.

scholarly journals Locally soluble groups with min-n.

1974 ◽  
Vol 17 (3) ◽  
pp. 305-318 ◽  
Author(s):  
H. Heineken ◽  
J. S. Wilson
Keyword(s):  
Soluble Group ◽  
Free Groups ◽  
Torsion Group ◽  
Minimal Condition ◽  
Normal Subgroups ◽  
Soluble Groups ◽  
Isomorphism Classes ◽  
Torsion Groups ◽  
Torsion Free ◽  
General Method

It was shown by Baer in [1] that every soluble group satisfying Min-n, the minimal condition for normal subgroups, is a torsion group. Examples of non-soluble locally soluble groups satisfying Min-n have been known for some time (see McLain [2]), and these examples too are periodic. This raises the question whether all locally soluble groups with Min-n are torsion groups. We prove here that this is not the case, by establishing the existence of non-trivial locally soluble torsion-free groups satisfying Min-n. Rather than exhibiting one such group G, we give a general method for constructing examples; the reader will then be able to see that a variety of additional conditions may be imposed on G. It will follow, for instance, that G may be a Hopf group whose normal subgroups are linearly ordered by inclusion and are all complemented in G; further, that the countable groups G with these properties fall into exactly isomorphism classes. Again, there are exactly isomorphism classes of countable groups G which have hypercentral nonnilpotent Hirsch-Plotkin radical, and which at the same time are isomorphic to all their non-trivial homomorphic images.

SOLUBLE GROUPS OF FINITE RANK

2004 ◽  
pp. 83-104
Author(s):  
John C. Lennox ◽  
Derek J. S. Robinson
Keyword(s):  
Finite Rank ◽  
Soluble Groups

A Geometric Characterization of Nonnegative Bands

2004 ◽  
Vol 47 (2) ◽  
pp. 257-263
Author(s):  
Alka Marwaha
Keyword(s):  
Invariant Subspace ◽  
Geometric Structure ◽  
Finite Rank ◽  
Special Kind ◽  
Maximal Rank ◽  
Geometric Characterization ◽  
Idempotent Operators ◽  
Rank One ◽  
Standard Subspace

AbstractA band is a semigroup of idempotent operators. A nonnegative band S in having at least one element of finite rank and with rank (S) > 1 for all S in S is known to have a special kind of common invariant subspace which is termed a standard subspace (defined below).Such bands are called decomposable. Decomposability has helped to understand the structure of nonnegative bands with constant finite rank. In this paper, a geometric characterization of maximal, rank-one, indecomposable nonnegative bands is obtained which facilitates the understanding of their geometric structure.

scholarly journals A characterization of finite p-soluble groups of p-length one by commutator identities

1981 ◽  
Vol 30 (3) ◽  
pp. 257-263 ◽  
Author(s):  
Rolf Brandl
Keyword(s):  
Finite Group ◽  
Classical Result ◽  
Soluble Groups ◽  
Similar Description ◽  
A Finite Group ◽  
Engel Condition ◽  
Almost All

AbstractA classical result of M. Zorn states that a finite group is nilpotent if and only if it satisfies an Engel condition. If this is the case, it satisfies almost all Engel conditions. We shall give a similar description of the class of p-soluble groups of p-length one by a sequence of commutator identities.

scholarly journals On soluble groups of module automorphisms of finite rank

2017 ◽  
Vol 67 (3) ◽  
pp. 809-818 ◽  
Author(s):  
Bertram A. F. Wehrfritz
Keyword(s):  
Finite Rank ◽  
Soluble Groups
Sign in / Sign up

Export Citation Format

Share Document