Soft Computing

, Volume 21, Issue 10, pp 2503–2505

An application of subgroup lattices

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Abstract

We give a lattice theoretic proof of the well-known result that a finite group G is cyclic iff G has at most one subgroup of each order dividing |G|. Consequently, we show that a division ring D is a field iff D has at most one maximal subfield.

Keywords

Subgroup lattice Distributive lattice Cyclic group Division ring Wedderburn’s “little” Theorem 

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of FoundationFujian Commercial CollegeFuzhouChina
  2. 2.Department of MathematicsBeihang UniversityBeijingChina

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