On characterizations of linear groups. I

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

چکیده ندارد.

On the Characterization of Linear and Projective Linear Groups. I

Overgroups of Irreducible Linear Groups, I

In work spread over several decades, Dynkin ([4, 3]), Seitz ([10, 11]), and Testerman ([16]) classified the maximal closed connected subgroups of simple algebraic groups. Their analyses for the classical group cases were based primarily on a striking result: If G is a simple algebraic group and φ : G SL V is a tensor indecomposable irreducible rational representation, then with specified except...

I. Characterizations of Freeness

Let M be a B-probability space. Assume that B itself is a D-probability space; then M can be viewed as D-probability space as well. Let X ∈ M. We look at the question of relating the properties of X as B-valued random variable to its properties as D-valued random variable. We characterize freeness of X from B with amalgamation over D: (a) in terms of a certain fac-torization condition linking t...

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.