Is the largest order of an element of a group always the size of the group?
99788
Why does a multiplicative subgroup of a field have to be cyclic?
38083
Order of conjugate of an element given the order of its conjugate
152604
For a finite group of order $2n$ does there exist $x$ such that $x\ast x=e$?
114187
In a finite cyclic group, the generator has the order of the group
33819
What does "the ${\bf N}$ of a group" mean?
112157
If $g$ is the generator of a group $G$, order $n$, when is $g^k$ a generator?
56234
Isomorphism $f$ preserves the order of an element?
67554
In a group, the number of non-self-inverse elements is even
95378
Known bounds for the number of groups of a given order.
158282
Finite order of an element $f(g)$ of a homomorphism $f$
16476
Order of the product of two commuting elements with coprime orders in a group.
81543
Finite abelian group contains an element with order equal to the lcm of the orders of its elements
14383
Order of Permutation : If $\tau \in S_n$ has order $m$, then $\sigma \tau\sigma^{-1}$ has also order $m$.
81406
Does every set have a group structure?
39976
If a group G has only the trivial group and G itself as its subgroup, can we be sure that G has prime order?
19668
Does every group whose order is a power of a prime p contain an element of order p?
126771
Group element not taken to its inverse by any automorphism