Search results for "algebra"
showing 10 items of 4129 documents
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.
A combinatorial algorithm related to the geometry of the moduli space of pointed curves
2002
As pointed out in Arbarello and Cornalba ( J. Alg. Geom. 5 (1996), 705–749), a theorem due to Di Francesco, Itzykson, and Zuber (see Di Francesco, Itzykson, and Zuber, Commun. Math. Phys. 151 (1993), 193–219) should yield new relations among cohomology classes of the moduli space of pointed curves. The coefficients appearing in these new relations can be determined by the algorithm we introduce in this paper.
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
On some recent investigations of probability in group theory
2010
We describe some recent contributions on the probability of commuting pairs, introduced by P. Erdos, W. Gustafson and P. Turan around 1968 and 1973. Both combinatorial methods and character theory have significant application in this context and we illustrate some standard techniques and strategies, once generalizations of the probability of commuting pairs want to be studied. The importance of the subject is emphasized in some remarks and open questions, which reformulate some classical conjectures in group theory via a probabilistic approach.