Find an alternate generating set for Dih(2n)
Recall that 
.
Show that every element of
which is not a power of 
has order 2. Deduce that is generated by the two elements 
and 
, both of which have order 2.
Let
be a non power of . By a previous exercise, we know that 
. Moreover, 
for some 
. Thus 
, hence 
.
Now note that
and 
since 
. Thus 
.
.Show that every element of
which is not a power of has order 2. Deduce that is generated by the two elements and , both of which have order 2.Let
be a non power of . By a previous exercise, we know that . Moreover, for some . Thus , hence .Now note that
and since . Thus .
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