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

Abstract.

In this article both sporadic Janko-groups J₂ and J₃ are constructed from their common involution centralizer $H \cong 2^{1+4}$ : A₅ 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.