We prove L boundedness of certain non-translation-invariant discrete maximal Radon transforms and discrete singular Radon transforms. We also prove maximal, pointwise, and L ergodic theorems for certain families of non-commuting operators.

Let G be a non-abelian group. The non-commuting graph AG of G is defined as the graph whose vertex set is the non-central elements of G and two vertices are joint if and only if they do not commute. In a finite simple graph Γ the maximum size of a complete subgraph of Γ is called the clique number of Γ and it is denoted by ω(Γ). In this paper we characterize all non-solvable groups G with ω(AG)...