Tuesday, July 5, 15:30, 7.527
Leo Margolis, Free subgroups in the integer group ring and dihedral p-critical elements.

Abstract:
In the recent years the construction of non-abelian free groups in the unit group of an intergral group ring was intensivley studied. Some of these results are presented here.
Approaching the construction of a non-abelian free group using Bass-cyclic units Angel del Rio and Jairo Goncalves defined a dihedral p-critical element g of a group G to be an element of prime order p, which is not only conjugate to g and g^{-1} in G, but is so in every subgroup and quotient group of G. Del Rio and Goncalves classified the solvable groups possesing dihedral p-critical elements. The non-solvable groups possesing such elements are simple and were classified using the CFSG by Robert Guralnick to be groups of the type PSL(2, q). We show how this result in some special cases can be achieved without the CFSG.