Finite simple groups with sylow 2-subgroup dihedral wreath Z2

Endotrivial Modules over Groups with Quaternion or Semi-dihedral Sylow 2-subgroup

Suppose that G is a finite group and that k is a field of characteristic p. Endotrivial kG-modules appear in a natural way in many areas surrounding local analysis of finite groups. They were introduced by Dade [14] who classified them in the case that G is an abelian p-group. A complete classification of endotrivial modules over the modular group rings of p-groups was completed just a few year...

Finite Groups with p-Sylow Coverings

A REDUCTION THEOREM FOR UNil OF FINITE GROUPS WITH NORMAL ABELIAN SYLOW 2-SUBGROUP

Let F be a finite group with a Sylow 2-subgroup S that is normal and abelian. Using hyperelementary induction and cartesian squares, we prove that Cappell’s unitary nilpotent groups UNil∗(Z[F ];Z[F ],Z[F ]) have an induced isomorphism to the quotient of UNil∗(Z[S];Z[S],Z[S]) by the action of the group F/S. In particular, any finite group F of odd order has the same UNil-groups as the trivial gr...

Reduction of UNil for finite groups with normal abelian Sylow 2-subgroup

Let F be a finite group with a Sylow 2-subgroup S that is normal and abelian. Using hyperelementary induction and cartesian squares, we prove that Cappell’s unitary nilpotent groups UNil∗(Z[F ];Z[F ],Z[F ]) have an induced isomorphism to the quotient of UNil∗(Z[S];Z[S],Z[S]) by the action of the group F/S. In particular, any finite group F of odd order has the same UNil-groups as the trivial gr...

A New Finite Simple Group with Abelian 2-sylow Subgroups.

A 2-Sylow subgroup of J is elementary abelian of order 8 and J has no subgroup of index 2. If r is an involution in J, then C(r) = (r) X K, where K _ A5. Let G be a finite group with the following properties: (a) S2-subgroups of G are abelian; (b) G has no subgroup of index 2; and (c) G contains an involution t such that 0(t) = (t) X F, where F A5. Then G is a (new) simple group isomorphic to J...