The notion of a plump subgroup was recently introduced by Amrutam. This is relativized version Powers' averaging property, and it known that property equivalent to C*-simplicity. With this in mind, we introduce C*-simplicity, show for normal subgroups plumpness, along with several other characterizations.

self etching primers, due to ease of manipulation, have been extensively used in recent years. these self etching primers containing a relatively weak acid, may not provide an optimal bond strength. the purpose of the present in-vitro investigation was to evaluate the effects of 37% phosphoric acid application prior to applying self etching primers on composite bond strength. in this experiment...

Let Za × Zb be the product of two directed cycles, let Zc be a subgroup of Za, and let Zd be a subgroup of Zb. Also, let A = a c and B =

If P is a p-group for some prime p we shall write M (P ) to denote the set of all maximal subgroups of P and Md(P ) = {P1, ..., Pd} to denote any set of maximal subgroups of P such that ∩d i=1 Pi = Φ(P ) and d is as small as possible. In this paper, the structure of a finite group G under some assumptions on the c-normal or s-quasinormally embedded subgroups in Md(P ), for each prime p, and Syl...

Let G = SO(n, 1)◦ for n ≥ 2 and Γ a geometrically finite Zariski dense subgroup of G which is contained in an arithmetic subgroup of G. Denoting by Γ(q) the principal congruence subgroup of Γ of level q, and fixing a positive number λ0 strictly smaller than (n − 1)/4, we show that, as q → ∞ along primes, the number of Laplacian eigenvalues of the congruence cover Γ(q)\H smaller than λ0 is at mo...