On groups of finite Prüfer rank

• Wehrfritz, B. A. F. ^[1]
  1. [1] Queen Mary University of London

     Queen Mary University of London

     Reino Unido

     
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 68, Nº. 2, 2024, págs. 439-443
• Idioma: inglés
• DOI: 10.5565/PUBLMAT6822405
• Enlaces
  • Texto completo
• Resumen

  • Let G be a group of finite rank and π any finite set of primes. We prove that G contains a characteristic subgroup H of finite index such that every finite π-image of H is nilpotent. Our conclusions are stronger if G is also soluble.

• Referencias bibliográficas
  • D. N. Azarov and N. S. Romanovski˘ı, Finite homomorphic images of groups of finite rank (Russian), Sibirsk. Mat. Zh. 60(3) (2019), 483–488;...
  • R. Brauer and W. Feit, An analogue of Jordan’s theorem in characteristic p, Ann. of Math. (2) 84(2) (1966), 119–131. DOI: 10.2307/1970514
  • J. D. Dixon, The Structure of Linear Groups, Van Nostrand Reinhold mathematical studies 37, Van Nostrand-Reinhold Inc., London, New York,...
  • M. R. Dixon, Sylow Theory, Formations and Fitting Classes in Locally Finite Groups, Ser. Algebra 2, World Scientific Publishing Co., Inc.,...
  • O. H. Kegel and B. A. F. Wehrfritz, Locally Finite Groups, North-Holland Math. Library 3, North-Holland Publishing Co., Amsterdam-London;...
  • J. C. Lennox and D. J. S. Robinson, The Theory of Infinite Soluble Groups, Oxford Math. Monogr., The Clarendon Press, Oxford University Press,...
  • B. A. F. Wehrfritz, Almost fixed-point-free automorphisms of prime order, Cent. Eur. J. Math. 9(3) (2011), 616–626. DOI: 10.2478/s11533-011-0017-z
  • B. A. F. Wehrfritz, On groups of finite rank, Publ. Mat. 65(2) (2021), 599–613. DOI: 10.5565/publmat6522106
  • B. A. F. Wehrfritz, Locally finite groups and a theorem of Belyaev, Adv. Group Theory Appl. 16 (2023), 109–115. DOI: 10.32037/agta-2023-011