Author/Authors :
Mahmoudifar, A. Department of Mathematics - North Tehran Branch - Islamic Azad University , Moghaddamfar, A. R Faculty of Mathematics - K. N. Toosi University of Technology , Salehzadeh, F. Faculty of Mathematics - K. N. Toosi University of Technology
Abstract :
Let G be a nonabelian group, A ⊂ G an abelian subgroup and
n > 2 an integer. We say that G has an n-abelian partition with respect to
A, if there exists a partition of G into A and n disjoint commuting subsets
A1, A2, . . . , An of G, such that |Ai| > 1 for each i = 1, 2, . . . , n. We classify
all nonabelian groups, up to isomorphism, which have an n-abelian partition,
for n = 2 and 3.
