Prove a group of order 12 must have an element of order 2
26398
Group of even order contains an element of order 2
2794
Prove that if a group contains exactly one element of order 2, then that element is in the center of the group.
46260
Prove that a group generated by two elements of order $2$, $x$ and $y$, is isomorphic to $D_{2n}$, where $n = |xy|.$
156319
Show that a group with $|G| = 33$ contains an element of order $3$
47478
Show that any cyclic group of even order has exactly one element of order $2$
25404
Let $G$ be a group of order $2m$ where $m$ is odd. Prove that $G$ contains a normal subgroup of order $m$
92750
Groups where all elements are order 3
107010
How many elements of order $k$ are in $S_n$?
13807
Is there a way to prove that the order of an element in a Group divides the order of the Group, WITHOUT USING LAGRANGE'S
46687
Elements of $GL_{2}(\mathbb{Z})$ of finite order
92968
how many element of order 2 and 5 are there
124224
How many groups of order $n$ with center {e} exist?
94420
Dihedral group - elements of order $2$
143550
Order of product of two elements in an abelian group
150156
Proving that $S_n$ has order $n!$
114522
Prove that identity is unique in a group
85579
$G$ a group s.t. every non-identity element has order 2. If $G$ is finite, prove $|G| = 2^n$ and $G \simeq C_2 \times C_2 \times\cdots\times C_2$