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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.

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