Mastery over the groups $S_n,A_n,D_n$ and $Q_8$

Question

I am a graduate student and currently preparing for PHD entrance in the leading institutes of India. For that I have to strengthen my group theory. But I must admit that I have a shaky foundation in group theory, specially the symmetric group, alternating group, dihedral group and quaternion group.

I do not have clear idea about the structure of these groups. I want some information about them, for example center, normal subgroups, Cayley digraph and subgroup lattice.

Can someone suggest me some book or note where I can find all these details? Also one can suggest me some notes or stack exchange pages for the same purpose.

Answer 1

A) Pick a standard book like :

1. Topics in Algebra by I. N. Herstein

2. Abstract Algebra Book by Dummit,Foote

3. Algebra Book by Thomas W. Hungerford

4. Algebra : A Graduate Course Book by Martin Isaacs

B) Expository papers by Keith Conard. (One of best resources on the web)

C) Group Explorer by Nathan Carter. ( Structure of finite groups of small order)

D) Search on Wikipedia by topic.

E) Finally MSE when you stuck.