On linear groups

on the effect of linear & non-linear texts on students comprehension and recalling

چکیده ندارد.

NSE characterization of some linear groups

‎For a finite group $G$‎, ‎let $nse(G)={m_kmid kinpi_e(G)}$‎, ‎where $m_k$ is the number of elements of order $k$ in $G$‎ ‎and $pi_{e}(G)$ is the set of element orders of $G$‎. ‎In this paper‎, ‎we prove that $Gcong L_m(2)$ if and only if $pmid |G|$ and $nse(G)=nse(L_m(2))$‎, ‎where $min {n,n+1}$ and $2^n-1=p$ is a prime number.

On the Characterization of Linear and Projective Linear Groups. I

Convolution of Discrete Measures on Linear Groups

Let p, q ∈ R such that 1 < p < 2 and 2 p = 1 + 1q . Define ‖f‖p = max x,G1 ( ∑ y∈G1 |f(xy)|p )1/p (*) where G1 is taken in some class of subgroups specified later. We prove the following two theorems about convolutions. Theorem 2. Let G = SL2(C) equipped with the discrete topology. Then there is a constant τ = τp > 0 such that for f ∈ `(G) ‖f ∗ f‖1/2 q ≤ C‖f‖1−τ p (‖f‖p) , where the maximum in ...

Arithmetic Results on Orbits of Linear Groups

Let p be a prime and G a subgroup of GLd(p). We define G to be pexceptional if it has order divisible by p, but all its orbits on vectors have size coprime to p. We obtain a classification of p-exceptional linear groups. This has consequences for a well known conjecture in representation theory, and also for a longstanding question concerning 1 2 -transitive linear groups (i.e. those having all...