Displaying 21 – 40 of 177

Showing per page

Finite groups with a unique nonlinear nonfaithful irreducible character

Ali Iranmanesh, Amin Saeidi (2011)

Archivum Mathematicum

In this paper, we consider finite groups with precisely one nonlinear nonfaithful irreducible character. We show that the groups of order 16 with nilpotency class 3 are the only p -groups with this property. Moreover we completely characterize the nilpotent groups with this property. Also we show that if G is a group with a nontrivial center which possesses precisely one nonlinear nonfaithful irreducible character then G is solvable.

Følner sequences in polycyclic groups.

Christophe Pittet (1995)

Revista Matemática Iberoamericana

The isoperimetric inequality |∂Ω| / |Ω| = constant / log |Ω| for finite subsets Ω in a finitely generated group Γ with exponential growth is optimal if Γ is polycyclic.

Groups with small deviation for non-subnormal subgroups

Leonid Kurdachenko, Howard Smith (2009)

Open Mathematics

We introduce the notion of the non-subnormal deviation of a group G. If the deviation is 0 then G satisfies the minimal condition for nonsubnormal subgroups, while if the deviation is at most 1 then G satisfies the so-called weak minimal condition for such subgroups (though the converse does not hold). Here we present some results on groups G that are either soluble or locally nilpotent and that have deviation at most 1. For example, a torsion-free locally nilpotent with deviation at most 1 is nilpotent,...

Currently displaying 21 – 40 of 177