Every Element of Order 2 is in the Center of a Group
2794
Prove that if a group contains exactly one element of order 2, then that element is in the center of the group.
100061
The Maximum possible order for an element $S_n$
13734
Show that every group of prime order is cyclic
92750
Groups where all elements are order 3
94999
A subgroup with an index of 2 is normal to the group.
58914
Any group of index 2 is normal
25832
Let $K$ be a normal subgroup of order 2 in group $G$, show that $K$ lies in the centre of $G$
96123
Element of maximal order in alternating group $A_{10}$: how to prove this is it?
79055
Orders of a symmetric group
105139
Verification of Proof that a nonabelian group G of order pq where p and q are primes has a trivial center
121423
Prove that every element of a finite group has an order
81354
The product of all the elements of a finite abelian group
75157
Every Group is a Fundamental Group
143550
Order of product of two elements in an abelian group
75568
Subgroup of index $2$ is Normal
157806
Order of a element on a Symmetric Group
30676
$G'$ and the product of all the elements in an odd order group