Example of non-abelian group with element have all order p prime?
121481
Non-abelian finite $p$-group in which every element has prime order?
35401
Examples of finite groups that are not a semidirect product
99309
Groups of order $n^2$ that have no subgroup of order $n$
105139
Verification of Proof that a nonabelian group G of order pq where p and q are primes has a trivial center
47239
For $p,q$ primes such that $q|p-1$, show there is only one non-abelian group of order $pq$, up to isomorphism
150188
Construct a non-abelian group of order 75
8742
Examples and further results about the order of the product of two elements in a group
49162
Classify all groups with order $pq$, $p$ is not equal to $q$
33593
An example of a non-abelian group $G$ where, for all $a,b\in G$, the equality $(ab)^{n}=a^{n}b^{n}$ holds for two consecutive integers $n$
14528
Proof that all abelian simple groups are cyclic groups of prime order
134455
Any group of order $15$ is abelian(without sylow theorem)
88718
A group is generated by two elements of order $2$ is infinite and non-abelian
47091
How to construct finite fields of any prime power order?
122335
Abelian $p$-group with unique subgroup of index $p$
39976
If a group G has only the trivial group and G itself as its subgroup, can we be sure that G has prime order?
6189
Examples of infinite groups such that all their respective elements are of finite order.
13734
Show that every group of prime order is cyclic