Title of article :
The probability of commuting subgroups in arbitrary lattices of subgroups
Author/Authors :
Kassaw Muhie, Seid Department of Mathematics and Applied Mathematics - University of Cape Town - South Africa , G. Russo, Francesco Department of Mathematics and Applied Mathematics - University of Cape Town - South Africa
Abstract :
A finite group G, in which two randomly chosen subgroups H and K commute, has been classified by Iwasawa in 1941. It is possible to define a probabilistic notion, which ``measures the distance'' of G from the groups of Iwasawa. Here we introduce the generalized subgroup commutativity degree gsd(G) for two arbitrary sublattices S(G) and T(G) of the lattice of subgroups L(G) of G. Upper and lower bounds for gsd(G) are shown and we study the behaviour of gsd(G) with respect to subgroups and quotients, showing new numerical restrictions.
Keywords
Keywords :
Subgroup commutativity degree , Dihedral groups , Sublattices , Elementary abelian p-groups , polynomial functions
Journal title :
International Journal of Group Theory
