Note on Generalized Schreier Extensions of Groups

Abstract

By a (generalized) Schreier extension we mean a group G decomposed into a subinvariant series Gn ↣ Gn-1 ↣ Gn-2 … ↣ G1 ↣ G0 = Gn is anti-invariant in G, i. e. the only subgroup of G which is normal in Gn is the trivial one. ( “ ↣ ” denotes a group monomorphism, i. e. an injection homomorphism. ) As is well known, such groups G can be embedded into the repeated wreath product where Fi ≅ Gi / Gi+1 (cf. [ 2 ], notation of M. Hall [ 1 ], p. 81).