Let G be a finite group. A complete Sylow product of G is a product of Sylow subgroups of G, one for each prime divisor of vertical bar G vertical bar. We shall call G a Sylow factorizable group if it is equal to at least one of its complete Sylow products. We prove that if G is a Sylow factorizable group then the intersection of all complete Sylow products of G is equal to the solvable radical of G. We generalize the concepts and the result to Sylow products which involve an arbitrary subset of the prime divisors of vertical bar G vertical bar.
展开▼