Some new characteristic p-functors and Thompson’s critical subgroup

Abstract

Let p be a prime and P be a finite p-group. We define a new characteristic subgroup K ( P ) of P and show that K ( P ) is a critical subgroup of P. Secondly, we define several new characteristic subgroups K * ( P ) , K i ( P ) for each positive integer i and show that they enjoy some interesting and new properties similar to the those of critical subgroups. Lastly, for a solvable group G, we define a new characteristic subgroup Y ( G ) , which satisfies the analogue of Thompson’s result for solvable groups.