Example of non-abelian group with element have all order p prime?
114535
what groups have only elements of prime order?
152820
Every element of a group has order $2$. Why, intuitively, is it abelian?
116080
Let G be a finite group with more than one element. Show that G has an element of prime order
126893
A group of order 2p (p prime) and other conditions - prove abelian.
157841
Existence of a non-abelian group of order $p^n$.
104080
Group with order $pq$ has subgroups of order $p$ and $q$
122335
Abelian $p$-group with unique subgroup of index $p$
38853
Cyclic group of prime order
53207
Let $p$ be a prime. If a group has more than $p − 1$ elements of order $p$, why can’t the group be cyclic?
134455
Any group of order $15$ is abelian(without sylow theorem)
61550
Existence of elements of order $p^k$ in a finite group
115449
Inclusion of Fields whose order is a prime power
103423
Normal subgroup where G has order prime
92899
$G$ is non abelian simple group of order $<100$ then $G\cong A_5$
150188
Construct a non-abelian group of order 75
143550
Order of product of two elements in an abelian group
53990
Group with more than one element and with no proper, nontrivial sub groups must have prime order.