Upper bounds for the number of irreducible character degrees of a group

Bounding the Number of Character Degrees of a Solvable Group

A difficult problem in the character theory of solvable groups is to show that the number c.d. (G) of irreducible character degrees of a solvable group G is equal to or greater than d.l. (G), the derived length of G. Isaacs [4] has shown that d.l. (G) ^ 3 c.d. (G)-2 for every solvable group. Berger [1] subsequently proved that d.l. (G) < c.d. (G) when | G | is odd. This problem belongs to the c...

On Finite Groups With Two Irreducible Character Degrees

Prime Divisors of Irreducible Character Degrees

Let G be a finite group. We denote by ρ(G) the set of primes which divide some character degrees of G and by σ(G) the largest number of distinct primes which divide a single character degree of G. We show that |ρ(G)| ≤ 2σ(G) + 1 when G is an almost simple group. For arbitrary finite groups G, we show that |ρ(G)| ≤ 2σ(G) + 1 provided that σ(G) ≤ 2.

investigating the feasibility of a proposed model for geometric design of deployable arch structures

deployable scissor type structures are composed of the so-called scissor-like elements (sles), which are connected to each other at an intermediate point through a pivotal connection and allow them to be folded into a compact bundle for storage or transport. several sles are connected to each other in order to form units with regular polygonal plan views. the sides and radii of the polygons are...

a study on the effectiveness of textual modification on the improvement of iranian upper-intermediate efl learners’ reading comprehension

این پژوهش به منظور بررسی تأثیر اصلاح متنی بر بهبود توانایی درک مطلب زبان آموزان ایرانی بالاتر از سطح میانی انجام پذیرفت .بدین منظور 115 دانشجوی مرد و زن رشته مترجمی زبان انگلیسی در این پزوهش شرکت نمودند.