Group of order $p^2$ with Center of order $p$
141125
Group with order $p^2$ must be abelian . How to prove that?
157582
Inverse of $ab$ and its order in a group with relations $a^2=e=b^6$ and $ab=b^4a$
19668
Does every group whose order is a power of a prime p contain an element of order p?
99205
Group of order $p^k q$ where $p$ and $q$ are distinct primes - how to prove this property?
75127
Group $G$ of order $p^2$: $\;G\cong \mathbb Z_{p^2}$ or $G\cong \mathbb Z_p \times \mathbb Z_p$
103423
Normal subgroup where G has order prime
91774
Existence of group $G$ with $|G|>2$ and automorphism group of odd order
13631
Showing group with $p^2$ elements is Abelian
62603
Characterizations of the $p$-Prüfer group
2731
Groups of even order have an element whose order is 2.
69820
A nontrivial p-group has nontrivial center
21568
Maximal order of an element in a symmetric group
4402
Group of order $pqr$, $p < q < r$ primes
114320
Showing that if the center of a group is trivial, then the center of its automorphism group is trivial
25832
Let $K$ be a normal subgroup of order 2 in group $G$, show that $K$ lies in the centre of $G$
7973
Groups of order $pq$ have a proper normal subgroup
88344
Order of a group and subsequent subgroups