Search results for "UPS"

Anti-$PC$-groups and Anti-$CC$-groups

2007

A groupGhas Černikov classes of conjugate subgroups if the quotient groupG/coreG(NG(H))is a Černikov group for each subgroupHofG. An anti-CCgroupGis a group in which each nonfinitely generated subgroupKhas the quotient groupG/coreG(NG(K))which is a Černikov group. Analogously, a groupGhas polycyclic-by-finite classes of conjugate subgroups if the quotient groupG/coreG(NG(H))is a polycyclic-by-finite group for each subgroupHofG. An anti-PCgroupGis a group in which each nonfinitely generated subgroupKhas the quotient groupG/coreG(NG(K))which is a polycyclic-by-finite group. Anti-CCgroups and anti-PCgroups are the subject of the present article.

On compact Just-Non-Lie groups

2007

A compact group is called a compact Just-Non-Lie group or a compact JNL group if it is not a Lie group but all of its proper Hausdorff quotient groups are Lie groups. We show that a compact JNL group is profinite and a compact nilpotent JNL group is the additive group of p -adic integers for some prime. Examples show that this fails for compact pronilpotent and solvable groups.

Probability of mutually commuting n-tuples in some classes of compact groups

2008

In finite groups the probability that two randomly chosen elements commute or randomly ordered n−tuples of elements mutually commute have recently attracted interest by many authors. There are some classical results estimating the bounds for this kind of probability so that the knowledge of the whole structure of the group can be more accurate. The same problematic has been recently extended to certain classes of infinite compact groups in [2], obtaining restrictions on the group of the inner automorphisms. Here such restrictions are improved for a wider class of infinite compact groups.

Isoclinism in probability of commuting n-tuples

2009

Strong restrictions on the structure of a group $G$ can be given, once that it is known the probability that a randomly chosen pair of elements of a finite group $G$ commutes. Introducing the notion of mutually commuting n-tuples for compact groups (not necessary finite), the present paper generalizes the probability that a randomly chosen pair of elements of $G$ commutes. We shall state some results concerning this new concept of probability which has been recently treated in [3]. Furthermore a relation has been found between the notion of mutually commuting n-tuples and that of isoclinism between two arbitrary groups.

A note on relative isoclinism classes of compact groups

2009

The generalized commutativity degree in a finite group

2009

On a result of L.-C. Kappe and M. Newell

2009

There is a long line of research investigating upper central series of a group. The interest comes from the information which these series can give on the structure of a group. Baer (1952) extended the usual notion of center of a group, introducing that of p-centre, where p is a prime. Almost 40 years later, Kappe and Newell (1989) were able to embed the p-centre of a metabelian p-group in the p-th term of the upper central series. This was possible because of the growing knowledge on Engel groups of the 60s years. Here we extend the result of Kappe and Newell (1989) to wider classes of groups.

The action of the unitary group associated with a quadratic extension of fields

1999

Given a quadratic extension L/k of fields of characteristic different from 2 and a unitary space (V, f) of finite dimension over L, we give a representation, as simple as possible, of the form which f induces by restriction on a k-substructure of V. This, in turn, allows one to study the orbits of the unitary group U(V, f) in the set of k-substructures of V of a given dimension.

On Geometric Simple Connectivity

2010

L'articolo intende dare una visione panoramica su ricerche recenti, molte delle quali sono da attribuire al V.Poenaru, sulla topologia di dimensione basse e sulla teoria geometrica dei gruppi.

Wielandt's results for algebraic k-groups

2006

We analyze the relation between subnormality and nilpotence, the subnormal joint property, some criteria of subnormality, the norm and the Wielandt subgroup in the case of algebraic groups defined over an arbitrary field.