Israel Journal of Mathematics

, Volume 9, Issue 3, pp 362–366 | Cite as

Groups whose proper factors are all abelian

  • T. Klein


The question implied in the title is a problem of A. Zaks, namely, which finite groups (other than abelian and simple groups) have all their proper factors abelian? This paper answers the question in the case of groups with non-trivial centre, or, equivalently, in the case ofp-groups, and gives a structure theorem for such groups.


Normal Subgroup Finite Group Simple Group Sylow Subgroup Structure Theorem 


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  1. 1.
    P. Hall,A contribution to the theory of groups of prime-power order Proc. London Math. Soc. (1933), 29–95.Google Scholar

Copyright information

© Hebrew University 1971

Authors and Affiliations

  • T. Klein
    • 1
  1. 1.Department of MathematicsTechnion-Israel Institute of TechnologyHaifa

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