$G$ is finite, $A \leq G$ and all double cosets $AxA$ have the same cardinality, show that $A \triangleleft G$
139096
$|AxA|$ is a constant implies normal subgroup
106927
How do I prove $[G:H\cap K]\leq [G:H][G:K]$?
109968
Let $X= \{ A \subset \mathbb{N} : \mathbb{N} \backslash A \text{ is finite}\}$. What is the cardinality of $X$? Prove it.
139835
Every Finite Group is Isomorphic to a Subgroup of $A_n$
89234
Any Set with Associativity, Left Identity, Left Inverse is a Group
83518
Proving Two sets have same cardinality
39165
Suppose $G$ is a group and $H,K \trianglelefteq G$. If $H \cap K =1$ the $hk=kh$ for all $k \in K, h \in H$?
10909
$|A \cup B| = \mathfrak{c}$, then $A$ or $B$ has cardinality $\mathfrak{c}$.
89167
Cardinality of equivalence relations in $\mathbb{N}$
93330
Cardinality of all cardinalities
70164
Proof exercise that the cardinal number of a set in $\mathbb R^2$ is $\frak c$
145873
Let $X$ and $Y$ be finite sets. Then the set $Y^X$ is finite and $\#(Y^X) = (\#Y)^{\#X}$.
30770
Prove that $C\left(\bigcup_{\alpha\in I} A_\alpha\right)=\bigcap_{\alpha\in I}C\left(A_\alpha\right)$
121141
Proving Finiteness of Group from Presentation
65098
Number of $\sigma$  -Algebra on the finite set
35800
If $K \leq H \leq G$, show that $[G:K] = [G:H][H:K]$.
58267
Godel's pairing function and proving c = c*c for aleph cardinals