Show that aH and bH contain the same number of elements in G
62687
Proving Cardinality of Cosets in Abstract Algebra
84198
Step in Proof of Cardinality of Product of two Groups
156319
Show that a group with $|G| = 33$ contains an element of order $3$
98542
Prove that $H$ is a subgroup of an abelian group $G$
77221
Prove that $G$ has a subgroup isomorphic to $G/H$.
130455
If $H,K⊲G$ and $H∩K = \{1_G\}$, then all elements in $H$ commute with all elements in $K$
83115
A set of elements in a reduced unity ring
10908
Associated elements in a ring
56245
Let H be a subgroup of a group G. Prove that the following statements are equivalent.
86336
For $G$ group and $H$ subgroup of finite index, prove that $N \subset H$ normal subgroup of $G$ of finite index exists
40852
Number of ways of distributing $n$ identical objects among $r$ groups
23579
If $G$ is isomorphic to $H$, then ${\rm Aut}(G)$ is isomorphic to ${\rm Aut}(H)$
13153
at least one element fixed by all the group
141379
All groups where underlying set has at most 4 elements
146421
How to prove a total order has a unique minimal element
118612
Neutral element in $\hom_C(A, B)$
141227
How to show the integers have same cardinality as the natural numbers?