International Journal of Modern Computation, Information and Communication Technology

ISSN 2581-5954

November 2018, Vol. 1, Issue 6, p. 111-115.​​

On Normal Intersection Conjugacy Functions in Finite 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: 


In the present paper, we investigate conjugacy classes of subgroups of a fixed but arbitrary group where the definition of these subgroups is made entirely within the structure of the group.  We have shown that these subgroups are analogous to F-injectors of the group where F is a locally defined Fitting class, but preclude the existence of such a class in their definition.  Moreover, the subgroups used to define the subgroups of such a conjugacy class are analogous to the F(p)-radicals of the group.

Keywords: Normal; Intersection; Conjugacy; Functions; Finite Group; Solvability.


  1. ​Conway JH, Curtis RT, Norton SP, Parker RA, Wilson RA. Atlas of finite groups. Oxford Univ. 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;307:565-9.
  3. Huppert B. Endliche Gruppen I Grundl. d. math. Wiss. 134. 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):731-4.
  7. Walls G. Trivial intersection groups. Arch Math 1979;32:1-4.
  8. Williams JS. Prime graph components of finite groups. J Algebra 1981;69:487-513.
  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.