We characterize finite-dimensional thick representations over $\mathbf{C}$ of connected complex semi-simple Lie groups by irreducible which are weight multiplicity-free and whose posets totally ordered sets. Moreover, using this characterization, we give the classification simple groups.

One of the great achievements of twentieth century mathematics is the classification of simple algebraic groups. These groups appear throughout mathematics and physics, as well as in chemistry and computer science. Groups often arise as symmetries of another object both inside and outside mathematics. A few specific cases include number theory, cryptography, algebraic geometry, algebraic topolo...

Abstract In this paper we apply social epistemology to mathematical proofs and their role in knowledge. The most famous modern collaborative proof effort is the Classification of Finite Simple Groups . history sociology have been well-documented by Alma Steingart (2012), who highlights a number surprising unusual features endeavour that set it apart from smaller-scale pieces mathematics. These ...

‎let $g$ be a finite $p$-group and $n$ be a normal subgroup of $g$ with‎ ‎$|n|=p^n$ and $|g/n|=p^m$‎. ‎a result of ellis (1998) shows‎ ‎that the order of the schur multiplier of such a pair $(g,n)$ of finite $p$-groups is bounded‎ ‎by $ p^{frac{1}{2}n(2m+n-1)}$ and hence it is equal to $‎ ‎p^{frac{1}{2}n(2m+n-1)-t}$ for some non-negative integer $t$‎. ‎recently‎, ‎the authors have characterized...