prove that in a cyclic group of even order, there is exactly one element of order 2.
47478
Show that any cyclic group of even order has exactly one element of order $2$
92057
Prove that for every odd integer n, there is a group...
36882
Two finite abelian groups with the same number of elements of any order are isomorphic
81354
The product of all the elements of a finite abelian group
109053
Show that a finite cyclic group of order $n$ has exactly one subgroup of order $d$ dividing $n$ and these are all the subgroups it has
86977
If $\cup \mathcal{F}=A$ then $A \in \mathcal{F}$. Prove that $A$ has exactly one element.
94420
Dihedral group - elements of order $2$
14528
Proof that all abelian simple groups are cyclic groups of prime order
126893
A group of order 2p (p prime) and other conditions - prove abelian.
156319
Show that a group with $|G| = 33$ contains an element of order $3$
28210
A finite group with exactly $2$ conjugacy classes isomorphic to $\mathbb{Z}_2$
54082
Group with exactly two subgroups of index 2
121423
Prove that every element of a finite group has an order
59811
Finite Abelian groups with the same number of elements for all orders are isomorphic
117468
$o(g^{k})=\frac{o(g)}{\gcd(o(g),k)}$ order of a power of a group element.
41731
Question about the order of the product of two elements in an abelian group
145406
Prove every element of $G$ has finite order.