A group of even order must contain an odd number of elements of order 2.
26398
Group of even order contains an element of order 2
118022
Show that a group of order $180$ is not simple.
124224
How many groups of order $n$ with center {e} exist?
104112
Number of finite simple groups of given order is at most $2$ - is a classification-free proof possible?
114662
Construction of a specific non-commutative and infinite group (with conditions on the order of the elements)
53990
Group with more than one element and with no proper, nontrivial sub groups must have prime order.
47478
Show that any cyclic group of even order has exactly one element of order $2$
38466
Proving that the number of vertices of odd degree in any graph G is even
94999
A subgroup with an index of 2 is normal to the group.
123065
Pretty way to group elements at odd and even positions
56607
gcd and order of elements of group
91774
Existence of group $G$ with $|G|>2$ and automorphism group of odd order
126113
Prove the existence of order 4 subgroups of order 8 groups
141379
All groups where underlying set has at most 4 elements
138862
Product of all elements in an odd finite abelian group is 1
1577
Order of nontrivial elements is 2 implies Abelian group
88718
A group is generated by two elements of order $2$ is infinite and non-abelian