Some results on generalized Baer-invariant of groups
Mohammad Reza R. Moghaddam, Mohammad Reza Rismanchian · Italian journal of pure and applied mathematics · 2002
Let V and W be two varities of groups defined by the sets of laws V and W, respectively. Then the generalized Baer-invariant with respect to two varieties will be introduced. If 1 → N → E → G → 1 is a group extension, it is shown that a factor group of N is a homomorphic image of the generalized Baer-invariant of the group G. Also the generalized Baer-invariant of the verbal factor group of G is determined, when the generalized Baer-invariant of G is trivial. Finally, a wide generalized version of Stallings theorem is obtained.