🛈 This materials is useful for Unit 2 in CSIR-NET and GATE Mathematical Sciences.

**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

- $ latex (\Bbb C- \{0\},.)$, where refers to multiplication of complex numbers.
- Integers modulo n,
- , the symmetric group.
- Any group of order < 6
- Any group of order where is prime.
- Any cyclic group is abelian.
- Any group of prime order is cyclic and hence abelian.

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### Counter-Examples (or Non-Abelian Groups)

- Symmetric groups
- , the group of Quaternions.
- , where .

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