Some Results on Baer's Theorem

Author

Department of Mathematics, Damghan University, Damghan, Iran.

Abstract

Baer has shown that, for a group G, finiteness of G=Zi(G) implies finiteness of ɣi+1(G). In this paper we will show that the converse is true provided that G=Zi(G) is finitely generated. In particular, when G is a finite nilpotent group we show that |G=Zi(G)| divides |ɣi+1(G)|d′ i(G), where d′i(G) =(d( G /Zi(G)))i.

Keywords

References

1. B.H. Neumann, Groups with nite classes of conjugate elements, Proc. London Math. Soc., 29, 236-248 (1954).
2. P. Niroomand, The converse of Schur's theorem, Arch. Math, 94, 401-403 (2010).
3. D. J. Robinson, A Course in the Theory of Groups, Springer-Verlag, Berlin (1982).
4. J. Wiegold, Multiplicators and groups with nite central factor-groups, Math. Z., 89, 345-347 (1965).
Analytical and Numerical Solutions for Nonlinear Equations
Volume 2, Issue 2
January 2018
Pages 151-155

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History

  • Receive Date: 08 January 2018
  • Accept Date: 08 January 2018

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