Let $G$ be a group of order $21$ contains contains an element $a$ of order $7$
133272
Number of normal subgroups of a non abelian group of order $21$... CSIR December $2013$
21568
Maximal order of an element in a symmetric group
68201
Cyclic group of order $n$
19352
Normal subgroup of index m contains every element of order n where m and n are relatively prime
121423
Prove that every element of a finite group has an order
32620
Is every group of order $21$ cyclic?
141379
All groups where underlying set has at most 4 elements
145127
For any integers $m,n>1$ , does there exist a group $G$ with elements $a,b \in G$ such that $o(a)=m , o(b)=n$ but $ab$ has infinite order ?
156319
Show that a group with $|G| = 33$ contains an element of order $3$
90329
Prove there is no simple group of order $729$
15526
Question on groups of order $pq$
61550
Existence of elements of order $p^k$ in a finite group
15633
If G is a group of even order, prove it has an element $a \neq e$ satisfying $a^2 = e$.
64269
Finding the minimal $n$ such that a given finite group $G$ is a subgroup of $S_n$
5089
An element of a group has the same order as its inverse
141458
How many subgroups or order 8 an abelian Group of order 72 can have
48393
Abelian groups of order n.