scholarly journals Finding characters satisfying a maximal condition for their unipotent support

2014 ◽  
Vol 218 (3) ◽  
pp. 474-496
Author(s):  
Jay Taylor
Keyword(s):  
Maximal Condition

On certain soluble groups

1969 ◽  
Vol 66 (1) ◽  
pp. 1-4 ◽  
Author(s):  
C. K. Gupta
Keyword(s):  
Normal Subgroups ◽  
Finitely Generated ◽  
Maximal Condition ◽  
Metabelian Groups ◽  
Soluble Groups ◽  
Finitely Generated Groups ◽  
The Law

In (2), Hall considered the question: for what varieties of soluble groups do all finitely generated groups satisfy max-n (the maximal condition for normal subgroups)? He has shown that the variety M of metabelian groups and more generally the variety of Abelian-by-nilpotent-of-class-c (c ≥ 1) groups has this property; whereas on the contrary, there are finitely generated groups in the variety V of centre-by-metabelian groups (i.e. defined by the law [x, y; u, v; z]) which do not satisfy max-n. One naturally raises the question: for what subvarieties of V do all finitely generated groups satisfy max-n?

scholarly journals A solution of a problem of Plotkin and Vovsi and an application to varieties of groups

1999 ◽  
Vol 67 (3) ◽  
pp. 329-355 ◽  
Author(s):  
C. K. Gupta ◽  
A. N. Krasil'nikov
Keyword(s):  
Free Group ◽  
Invariant Subgroup ◽  
Arbitrary Field ◽  
Finitely Based ◽  
Maximal Condition ◽  
Infinite Rank ◽  
Characteristic 2 ◽  
Countably Infinite ◽  
Fully Invariant Subgroups ◽  
Relatively Free Group

AbstractLet K be an arbitrary field of characteristic 2, F a free group of countably infinite rank. We construct a finitely generated fully invariant subgroup U in F such that the relatively free group F/U satisfies the maximal condition on fully invariant subgroups but the group algebra K (F/U) does not satisfy the maximal condition on fully invariant ideals. This solves a problem posed by Plotkin and Vovsi. Using the developed techniques we also construct the first example of a non-finitely based (nilpotent of class 2)-by-(nilpotent of class 2) variety whose Abelian-by-(nilpotent of class at most 2) groups form a hereditarily finitely based subvariety.

scholarly journals Soluble groups in which every finitely generated subgroup is finitely presented

1978 ◽  
Vol 26 (1) ◽  
pp. 115-125 ◽  
Author(s):  
J. R. J. Groves
Keyword(s):  
Subject Classification ◽  
Normal Subgroups ◽  
Finitely Generated ◽  
Maximal Condition ◽  
Soluble Groups ◽  
Image Position ◽  
Finitely Presented

AbstractThe class of finitely generated soluble coherent groups is considered. It is shown that these groups have the maximal condition on normal subgroups and can be characterized in a number of ways. In particular, they are precisely the class of finitely generated soluble groups G with the property:Subject classification (Amer. Math. Soc. (MOS) 1970): primary 20 E 15; secondary 20 F 05.

On Groups Saturated with Abelian Subgroups

1998 ◽  
Vol 08 (04) ◽  
pp. 443-466 ◽  
Author(s):  
Lev S. Kazarin ◽  
Leonid A. Kurdachenko ◽  
Igor Ya. Subbotin
Keyword(s):  
Finite Groups ◽  
Abelian Groups ◽  
Normal Subgroups ◽  
Main Subject ◽  
Maximal Condition ◽  
Locally Finite ◽  
Locally Finite Groups ◽  
Locally Nilpotent ◽  
Abelian Subgroups ◽  
Weak Maximal Condition

Groups with the weak maximal condition on non-abelian subgroups are the main subject of this research. Locally finite groups with this property are abelian or Chemikov. Non-abelian groups with the weak maximal condition on non-abelian subgroups, which have an ascending series of normal subgroups with locally nilpotent or locally finite factors, are described in this article.

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