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2 results

  • COMPONENTS AND MINIMAL NORMAL SUBGROUPS OF FINITE AND PSEUDOFINITE GROUPS

  • JOHN S. WILSON
  • Journal:
    The Journal of Symbolic Logic / Volume 84 / Issue 1 / March 2019
    Published online by Cambridge University Press:
    14 March 2019, pp. 290-300
    Print publication:
    March 2019

  • It is proved that there is a formula $\pi \left( {h,x} \right)$ in the first-order language of group theory such that each component and each non-abelian minimal normal subgroup of a finite group G is definable by $\pi \left( {h,x} \right)$ for a suitable element h of G; in other words, each such subgroup has the form $\left\{ {x|x\pi \left( {h,x} \right)} \right\}$ for some h. A number of consequences for infinite models of the theory of finite groups are described.