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​International Journal of Modern Computation, Information and Communication Technology

ISSN 2581-5954

​October 2018, Vol. 1, Issue 5, p. 93-98.​​

On Characterization of Various Finite Subgroups of Abelian Groups  
N. B. Okelo*
School of Mathematics and Actuarial Science, Jaramogi Oginga Odinga University of Science and Technology, P. O. Box 210-40601, Bondo-Kenya.
*Corresponding author’s e-mail: bnyaare@yahoo.com     

Abstract

The present paper, we characterize finite subgroups. Throughout G always denote a finite group. Let H be a subgroup group of G. We have H ≥ H ∩  1, for any x ϵ G. We call H to be a TI-subgroup of G if H ∩ Hx = H or 1 for any x ϵ G. We have shown that if H is normal in G or if H is of a prime order, then H is a TI-subgroup.

Keywords: Group; Finite group; TI-subgroup; Abelian group.

References

  1. ​Conway JH, Curtis RT, Norton SP, Parker RA, Wilson RA. Atlas of finite groups, Oxford University Press (Clarendon), Oxford and New York; 1985.
  2. Guo X, Li S, Flavell P.  Finite groups whose abelian subgroups are TI-subgroup. J Algebra 2007;307:565-69.
  3. Huppert B, Endlich GI. Springer-Verlag, Berlian Heidelberg, New York; 1979.
  4. Huppert B, Blackburn N. Finite groups III, Springer-Verlag, Berlin Heidelberg, New York; 1982.
  5. Isaacs IM. Character Theory of Finite Groups, Academic Press, New York; 1976.
  6. Li S, Guo X. Finite p-groups whose abelian subgroups have a trivial intersection. Acta Math. Sin 2007;23(4):731-34.
  7. Walls G. Trivial intersection groups. Arch Math 1979;32:1-4.
  8. Williams JS. Prime graph components of finite groups J Algebra 1981;69:487-13.
  9. Vijayabalaji S, Sathiyaseelan N. Interval-Valued Product Fuzzy Soft Matrices and its Application in Decision Making, Int J Mod Sci Technol 2016;1(7):159-63​​.
  10. Chinnadurai V, Bharathivelan K. Cubic Ideals in Near Subtraction Semigroups. Int J Mod Sci Technol 2016;1(8):276-82​​.