Show that an operation of elements in a finite group contains each elements exactly once
64527
Show that an operation of elements in a finite group contains each element exactly once
92057
Prove that for every odd integer n, there is a group...
21568
Maximal order of an element in a symmetric group
5226
Prove that a finite semigroup G with identity is a group if and only if G contains only one idempotent
130455
If $H,K⊲G$ and $H∩K = \{1_G\}$, then all elements in $H$ commute with all elements in $K$
121141
Proving Finiteness of Group from Presentation
64269
Finding the minimal $n$ such that a given finite group $G$ is a subgroup of $S_n$
47478
Show that any cyclic group of even order has exactly one element of order $2$
36882
Two finite abelian groups with the same number of elements of any order are isomorphic
112974
The $h-$th power of every element in a finite group of order $h$ is the identity element of the group
106660
Every subgroup of the integers has finite index
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
2794
Prove that if a group contains exactly one element of order 2, then that element is in the center of the group.
67926
$S_n$ is generated by elements of the form $(1k)$
157806
Order of a element on a Symmetric Group
139912
Complexity of finite group isomorphism problem
31252
"Efficient version" of Cayley's Theorem in Group Theory