Search results for "commutativity degree"
showing 7 items of 7 documents
Relative $n$-isoclinism classes and relative nilpotency degree of finite groups
2013
$n$-th relative nilpotency degree and relative $n$-isoclinism classes
2011
P. Hall introduced the notion of isoclinism between two groups more than 60 years ago. Successively, many authors have extended such a notion in different contexts. The present paper deals with the notion of relative n-isoclinism, given by N. S. Hekster in 1986, and with the notion of n-th relative nilpotency degree, recently introduced in literature.
A probabilistic meaning of certain quasinormal subgroups
2007
The role of the cyclic quasinormal subgroups has been recently described in groups both finite and infinite by S.Stonehewer and G.Zacher. This role can be better analyzed in the class of compact groups, obtaining restrictions for the probability that two randomly chosen elements commute. Mathematcs Subject Classification: 20D60, 20P05, 20D08
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.