A necessary condition is given for a very wide separable p-group to be derermined by its n-socle (the set of elements of order at mostpn). A group G is very wide if it has a direct summand of final rank ‖G‖ which itself is a direct sum of cyclic groups. In the case, n=1 (as Shelat has shown)this condition is sufficient but for n1 examples are given to show that this condition is not sufficient.
展开▼
