Normal subgroup of a finite group
Source: Schweitzer 2009
November 13, 2009
group theoryabstract algebrainductiongeometrygeometric transformationlinear algebramatrix
Problem Statement
Let be a finite non-commutative group of order t \equal{} 2^nm, where are positive and is odd. Prove, that if the group contains an element of order , then
(i) is not simple;
(ii) contains a normal subgroup of order .