Show a group cannot have order $2n$ for some odd $n\gt 1$ and be simple (without Cauchy's Theorem)
52089
Group of $2n$ elements, $n$ odd, is not simple
86893
Show that it is impossible to list the rational numbers in increasing order
62977
Show on $\mathbb{N}$ there are $2^{\aleph_0}$ nonisomorphic linear orders.
85579
$G$ a group s.t. every non-identity element has order 2. If $G$ is finite, prove $|G| = 2^n$ and $G \simeq C_2 \times C_2 \times\cdots\times C_2$
63499
Groups of prime squared order
48393
Abelian groups of order n.
15633
If G is a group of even order, prove it has an element $a \neq e$ satisfying $a^2 = e$.
53409
Show group of order $4n + 2$ has a subgroup of index 2.
68201
Cyclic group of order $n$
1577
Order of nontrivial elements is 2 implies Abelian group
59561
Suppose that G is a group and N < G a normal subgroup. Prove G/N is simple
150156
Proving that $S_n$ has order $n!$
88718
A group is generated by two elements of order $2$ is infinite and non-abelian
30676
$G'$ and the product of all the elements in an odd order group
105139
Verification of Proof that a nonabelian group G of order pq where p and q are primes has a trivial center
116737
An element of a group $G$ is not conjugate to its inverse if $\lvert G\rvert$ is odd
50706
$|G|=p(p+1)$ for $p$ prime, then $G$ has a normal subgroup of order $p$ or $p+1$