Prove that $S_5$ has no elements of order $120$.
100061
The Maximum possible order for an element $S_n$
113695
Show that there is no integer n with $\phi(n)$ = 14
64518
Prove $S_4$ has only 1 subgroup of order 12
118022
Show that a group of order $180$ is not simple.
99908
When does $120$ divide $n^5 - n$
22977
How many $6$-integer subsets of $\{1, 2, 3, \ldots, 20\}$ have no consecutive integers?
140106
How to prove a finite field is not ordered?
119808
Proving that $n$-cycle has order $n$
84491
Finding the smallest positive integer $n$ such that $S_n$ contains an element of order 60.
144802
Prove no solution to $x^2\equiv3\bmod5$
83178
Matrix Group induction proof and order of elements question
89452
Proof about Graph with no triangle
47799
Show that the number or $r$ combinations of $X$ which contain no consecutive integers is given by $\binom{n-r+1}{r}$
77198
Showing that the characteristic of a commutative ring R without zero divisors is 0 or prime
36862
A question about proving that there is no greatest common divisor
74281
Proof there is no largest cardinal number
125604
Proof that $\mathbb{Z}$ has no zero divisors