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Monatshefte für Mathematik

, Volume 185, Issue 1, pp 87–101 | Cite as

Note on Caranti’s method of construction of Miller groups

  • Rahul Dattatraya Kitture
  • Manoj K. Yadav
Article
  • 99 Downloads

Abstract

The non-abelian groups with abelian group of automorphisms are widely studied. Following Earnley, such groups are called Miller groups, since the first example of such a group was given by G.A. Miller in 1913. Many other examples of Miller p-groups have been constructed by several authors. Recently, Caranti (Isr J Math 205: 235–246, 2015) provided module theoretic methods for constructing non-special Miller p-groups from special Miller p-groups. By constructing examples, we show that these methods do not always work. We also provide a sufficient condition on special Miller p-group for which the methods of Caranti work.

Keywords

p-group Central automorphism Automorphism group 

Mathematics Subject Classification

20D45 20D15 

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Copyright information

© Springer-Verlag Wien 2016

Authors and Affiliations

  1. 1.School of MathematicsHarish-Chandra Research InstituteAllahabadIndia

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