- #1
astronut24
- 10
- 0
if a group of order 2p ( p prime) is abelian...then does it have exactly one element of order 2 ?? if a group is non abelian...i could figure out that there are p elements of order 2. but the abelian case is a bit confusing...
also..is it like...any group of order 2p has an element of order p?
if a group has orer p^a , a>=1 where p is prime...then I've got to show that G has an element of order p.
can i say that any non-identity element in G can have order p or p^2 or p^3...or p^a. then if x in G is of the form x^(p^i) =e ...we can say, (x^(p^(i-1))^p= e and we've found an element x^(p^(i-1)) that is of order p...it seems too simple to be correct.
also..is it like...any group of order 2p has an element of order p?
if a group has orer p^a , a>=1 where p is prime...then I've got to show that G has an element of order p.
can i say that any non-identity element in G can have order p or p^2 or p^3...or p^a. then if x in G is of the form x^(p^i) =e ...we can say, (x^(p^(i-1))^p= e and we've found an element x^(p^(i-1)) that is of order p...it seems too simple to be correct.