Israel Journal of Mathematics

, Volume 40, Issue 3, pp 307–323

Sylow-metacyclic groups andQ-admissibility

Authors

  • David Chillag
    • Department of MathematicsTechnion — Israel Institute of Technology
  • Jack Sonn
    • Department of MathematicsTechnion — Israel Institute of Technology
Article

DOI: 10.1007/BF02761371

Cite this article as:
Chillag, D. & Sonn, J. Israel J. Math. (1981) 40: 307. doi:10.1007/BF02761371

Abstract

A finite groupG isQ-admissible if there exists a division algebra finite dimensional and central overQ which is a crossed product forG. AQ-admissible group is necessarily Sylow-metacyclic (all its Sylow subgroups are metacyclic). By means of an investigation into the structure of Sylow-metacyclic groups, the inverse problem (is every Sylow-metacyclic groupQ-admissible?) is essentially reduced to groups of order 2a 3b and to a list of known “almost simple” groups.

Copyright information

© The Weizmann Science Press of Israel 1981