On Stability of the Cauchy Functional Equation in Groupoids

We give some stability results for the functional equation $\textit{a(xy) = a(x) + a(y)}$, where $\textit{a: G -> E, G}$ being a groupoid and $\textit{E}$ a Banach space

L9L_9-free groups

In this article we classify all $L_9$-free finite groups

Finite simple 3′-groups are cyclic or Suzuki groups, preprint, 2013. Alfréd Rényi Institute of Mathematics, Reáltanoda utca 13-15

In this note we prove that all finite simple 3 ′ -groups are cyclic of prime order or Suzuki groups. This is well known in the sense that it is mentioned frequently in the literature, often referring to unpublished work of Thompson. Recently an explicit proof was given by Aschbacher ([3]), as a corollary of the classification of S 3 -free fusion systems. We argue differently, following Glauberman's comment in the preface to the second printing of his bookle