3.1.01
July 23, 2019
The preimage of a subgroup under a homomorphism is a subgroup.
3.1.36
June 19, 2019
Prove that if \(G/Z(G)\) is cyclic then \(G\) is abelian.
3.2 More on Cosets and Lagrange's Theorem
May 6, 2019
3.3 The Isomorphism Theorems
May 11, 2019
3.4 Composition Series and the Hölder Program
July 31, 2019
3.4.01
August 3, 2019
Prove that if \(G\) is an abelian simple group, then \(G \cong Z_p\) for some prime \(p\). Do not assume \(G\) is a finite group.
3.4.06
August 9, 2019
Prove part (1) of the Jordan-Hölder Theorem by induction on \(|G|\).
3.4.07
August 14, 2019
If \(G\) is a finite group and \(H \le G\) prove that there is a composition series of \(G\), one of whose terms is \(H\).
3.4.09
August 14, 2019
Prove the following special case of part (2) of the Jordan-Hölder Theorem...