let G be a finite nonabelian group and h be a subgroup of G. suppose that the order of H is p where p is a prime
(1)prove that H is abelian
(2)How many elements of H have order P?
(3)Suppose K is a subgroup of G with order q, where q is a prime and q doesn't equal p. what is H intersect K?
for(1) to prove h is abelian, I can show H is cyclic, but how to show H is cyclic?(because order of H is prime?)
for (2). the order of the elements of H is divisor of p, since p is prime, so there are p-1 elements since there is only one element order is 1 which is identity. is that right?
I have no idea how to do (3)
(1)prove that H is abelian
(2)How many elements of H have order P?
(3)Suppose K is a subgroup of G with order q, where q is a prime and q doesn't equal p. what is H intersect K?
for(1) to prove h is abelian, I can show H is cyclic, but how to show H is cyclic?(because order of H is prime?)
for (2). the order of the elements of H is divisor of p, since p is prime, so there are p-1 elements since there is only one element order is 1 which is identity. is that right?
I have no idea how to do (3)