An Introduction to Theory of Groups by Joseph J. Rotman - Exercise 1.5
75461
If $n>m$, then the number of $m$-cycles in $S_n$ is given by $\frac{n(n-1)(n-2)\cdots(n-m+1)}{m}$.
31252
"Efficient version" of Cayley's Theorem in Group Theory
86336
For $G$ group and $H$ subgroup of finite index, prove that $N \subset H$ normal subgroup of $G$ of finite index exists
39100
Exercise from Serre's "Trees" - prove that a given group is trivial
68971
Elementary approach to proving that a group of order 9 is Abelian
111049
Groups with given automorphism groups
81864
Finite group of order $mn$ with $\gcd(m,n) = 1$ .
152630
showing that a group of order 45 is abelian
68955
Characterising subgroups of Prüfer $p$-groups.
73382
A concrete example of involution in group theory
68422
Understanding Lagrange's Theorem (Group Theory)
62386
Theorem 5.1. Chapter I in Hartshorne Book's
114662
Construction of a specific non-commutative and infinite group (with conditions on the order of the elements)
933
How many groups exist with order $n$ (two isomorphic groups are treated as the same group)
37971
Prove that the center of a group is a normal subgroup
64582
Group covered by finitely many cosets
73113
Groups and Symmetries