Given a topological group G that can be embedded as subgroup into some vector space (over the field of reals) we say has invariant linear span if all spans under arbitrary embeddings spaces are isomorphic spaces. For an set A let $${{\mathbb {Z}}}^{(A)}$$ direct sum |A|-many copies discrete integers endowed with Tychonoff product topology. We show span. This answers question from paper Dikranja...

Let C1,…,Ce be noncentral conjugacy classes of the algebraic group G=SLn(k) defined over a sufficiently large field k, and let Ω:=C1×…×Ce. This paper determines necessary sufficient conditions for existence tuple (x1,…,xe)∈Ω such that 〈x1,…,xe〉 is Zariski dense in G. As consequence, new result concerning generic stabilizers linear representations groups proved, existing results on random (r,s)-...

Abstract In this paper we characterize, in terms of their conjugacy classes, linear groups G such that $$G/\zeta _k(G)$$ G / ζ k ( ) belongs to a certain group class $$\mathfrak {...