# Normal closure of 2-subnormal subgroup of prime order in nilpotent group is abelian

From Groupprops

## Statement

Suppose is a nilpotent group and is a 2-subnormal subgroup (?) of of order for some prime number . Then, the Normal closure (?) of in is an abelian group.

## Related facts

### Stronger facts

- Normal closure of 2-subnormal subgroup of prime order is abelian: We can
*drop*the assumption of the whole group being nilpotent. - Normal closure of 2-subnormal subgroup of prime power order in nilpotent group has nilpotency class at most equal to prime-base logarithm of order