•  31
    On the Schur-zassenhaus theorem for groups of finite Morley rank
    with Ali Nesin
    Journal of Symbolic Logic 57 (4): 1469-1477. 1992.
    The Schur-Zassenhaus Theorem is one of the fundamental theorems of finite group theory. Here is its statement:Fact1.1 (Schur-Zassenhaus Theorem). Let G be a finite group and let N be a normal subgroup of G. Assume that the order ∣N∣ is relatively prime to the index [G:N]. Then N has a complement in G and any two complements of N are conjugate in G.The proof can be found in most standard books in group theory, e.g., in [S, Chapter 2, Theorem 8.10]. The original statement stipulated one ofNorG/Nto…Read more
  •  26
    Schur-zassenhaus theorem revisited
    with Ali Nesin
    Journal of Symbolic Logic 59 (1): 283-291. 1994.
    One of the purposes of this paper is to prove a partial Schur-Zassenhaus Theorem for groups of finite Morley rank.Theorem 2.Let G be a solvable group of finite Morley rank. Let π be a set of primes, and let H ⊲ G a normal π-Hall subgroup. Then H has a complement in G.This result has been proved in [1] with the additional assumption thatGis connected, and thought to be generalized in [2] by the authors of the present article. Unfortunately in the last section of the latter paper there is an irrep…Read more