Uniform and natural existence proofs for Janko‚s sporadic groups J2 and J3

Abstract

In this article both sporadic Janko-groups J 2 and J 3 are constructed from their common involution centralizer H ∼ = 2 1+4 : A 5 within one single run of Michler's deterministic algorithm described in [11]. At the beginning we choose the -in some sense -most natural point to start from, and in the end we realize that Michler's algorithm does not necessary lead us to a simple group but sometimes to a covering group of a simple group.

On the Construction of the Finite Simple Groups with a Given Centralizer of a 2-Central Involution

“…In [14] Kratzer gave an existence proof for the Rudvalis group Ru by means of Algorithm 4.6. These results and the results of [15,16] show that all the steps of Algorithm 4.6 can be performed for all the finite sporadic groups not contained in the Monster: J 1 , J 3 , Ly, ON, Ru, and J 4 . This work of the author and his collaborators is in progress.…”