$G$ finite group of order $n$. What's the least $l<n$ such that $G$ embeds in $S_l$?
64269
Finding the minimal $n$ such that a given finite group $G$ is a subgroup of $S_n$
157819
Every group of order $56$ has a proper non - trivial normal subgroup?
86336
For $G$ group and $H$ subgroup of finite index, prove that $N \subset H$ normal subgroup of $G$ of finite index exists
15341
Non-abelian finite group in which more than half of the elements have order $2$
103423
Normal subgroup where G has order prime
52121
Let $G$ be a finite group with $|G|>2$. Prove that ${\rm Aut}(G)$ contains at least two elements.
131594
Can the symmetric group $S_n$ be imbedded as a subgroup in $A_{n+1}$?
91774
Existence of group $G$ with $|G|>2$ and automorphism group of odd order
85579
$G$ a group s.t. every non-identity element has order 2. If $G$ is finite, prove $|G| = 2^n$ and $G \simeq C_2 \times C_2 \times\cdots\times C_2$
79055
Orders of a symmetric group
122125
Order of group element divides order of finite group
15526
Question on groups of order $pq$
60075
Does there exist an $n$ such that all groups of order $n$ are Abelian?
101735
A finite $p$-group cannot be simple unless it has order $p$
157841
Existence of a non-abelian group of order $p^n$.
56607
gcd and order of elements of group
114590
Prove that any finite group $G$ of even order contains an element of order $2.$