Show that the element $φ(a)\in G'$ has also order d!
131946
Order of an Element Under a Homomorphism
83452
Prove that any conjugate of $a$ has the same order as $a$.
46260
Prove that a group generated by two elements of order $2$, $x$ and $y$, is isomorphic to $D_{2n}$, where $n = |xy|.$
22995
Let f:G to H be 1-1 homomorphism show that order of f(a) divides the order of G.
15526
Question on groups of order $pq$
53263
Show $\sum\limits_{d|n}\phi(d) = n$.
116080
Let G be a finite group with more than one element. Show that G has an element of prime order
34713
Suppose $f(n)$ is $O(g(n))$ and $d(n)$ is $O(e(n))$. How do i use Big O to show that $f (n)$ + $d(n)$ is $O(g(n) + e(n))$?
38083
Order of conjugate of an element given the order of its conjugate
38153
Looking for a simple proof that groups of order $2p$ are up to isomorphism $\mathbb{Z}_{2p}$ and $D_{p}$ .
96123
Element of maximal order in alternating group $A_{10}$: how to prove this is it?
12667
How many subgroups of order $n$ does $D_n$ have?
145406
Prove every element of $G$ has finite order.
81116
$gh = hg, \ \gcd(|g|, |h|) = 1\Rightarrow|gh| = |g||h|\ \ (|a|$ = order of element $a)$
94558
Show that $\phi(mn) = \phi(m)\phi(n)\frac{d}{\phi(d)}$
158282
Finite order of an element $f(g)$ of a homomorphism $f$
65096
$\chi(G)+\chi(G')\leq n+1$