# DM-Groups and Lattice-Q1

+5 votes

Let G be non-abelian group. $Min\{ |G| \}$ is ---?

asked Jul 8, 2019 2 flags
reshown Jul 9, 2019

## 3 Answers

–5 votes
6 is correct one
answered Jul 9, 2019 by (34,730 points) 4 flags
i didnt understand the question
can you explain?
How ? May you explain?
0 votes
Why a group with 5 elements can not be abelian?
answered Jul 10, 2019 by (130 points)
Every group with 5 element is abelian group
But in the link the group is taken to be a cyclic group. But in the question it is not mentioned.
+12 votes

When n=1 the group is a trivial one.

Now every group of prime order is cyclic and hence abelian. Hence groups of n=2,3 and 5 are abelian.

Since every group of order  p^2 (where p is prime) is abelian. Group of order 4= 2^2 is abelian.

Hence every group of order less than or equal to 5 is abelian.

Therefore smallest is 6

answered Jul 11, 2019 by (16,650 points)
How can you form a group with just 1 element ?
@soumyadeeppro20
The single element of the trivial group is the identity element.
https://en.wikipedia.org/wiki/Trivial_group
Can a single element form a "lattice"?
NO. It will not form a lattice.
Can you prove Why size 6 group is not abelian?
Answer: