Examples and Counter Examples for Abelian Groups

Note: This is the first of “Examples and Counter Examples” series. I plan on expanding such posts in course of time, as I come across examples.

Interesting fact: These are the OEIS lists of number of distinct groups of order n: number of groups,number of abelian groups, number of non-abelian groups

Examples

1. $\Bbb Z$
2. $\Bbb Q$
3. $\Bbb R$
4. Integers modulo n $\Bbb Z / n \Bbb Z$
5. $S_n,n\le2$, the symmetric group.
6. $A_n \subset S_n,\forall n\ge1$
7. Any group of order < 4

Counter-Examples (or Non-Abelian Groups)

1. Symmetric groups $S_n,n\ge3$

New kid in the block

Welcome the new kid in the block.

Almost two and a half years ago I kicked off my first WordPress blog Far Far Away, an attempt to showcase and improve my writing skills, and thankfully it was decently received in its first year before I got lazy and stopped writing regularly.

Off late I have been fascinated by the idea of “maths blogging” which is expected to improve my maths writing skills, and help me improve my skills in communicating mathematics. Thankfully WordPress.com supports $LaTeX$ (\LaTeX fails to render though).

For the record, this is my sixth or seventh blog, and second to hopefully survive my wrath and an attempt to learn writing maths. I am a maths post graduate.

I have also transferred my following tech posts from Far Far Away, an attempt to make that blog more focussed on non-maths, non-tech content:

I hope I will be able to be able to post more frequently after December 20th. Since then, I plan on at least one post a week.

The content will be mostly about (and not restricted to),