International Journal of Modern Computation, Information and Communication Technology
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: email@example.com
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.
- Conway JH, Curtis RT, Norton SP, Parker RA, Wilson RA. Atlas of finite groups. Oxford Univ. Press (Clarendon), Oxford and New York 1985.
- Guo X, Li S, Flavell P. Finite groups whose abelian subgroups are TI-subgroup. J Algebra 2007;307:565-9.
- Huppert B. Endliche Gruppen I Grundl. d. math. Wiss. 134. Springer-Verlag, Berlian Heidelberg, New York; 1979.
- Huppert B, Blackburn N. Finite groups III. Springer-Verlag, Berlin Heidelberg, New York; 1982.
- Isaacs IM. Character Theory of Finite Groups. Academic Press, New York; 1976.
- Li S, Guo X. Finite p-groups whose abelian subgroups have a trivial intersection. Acta Math Sin 2007;23(4):731-4.
- Walls G. Trivial intersection groups. Arch Math 1979;32:1-4.
- Williams JS. Prime graph components of finite groups. J Algebra 1981;69:487-513.
- 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.
- Chinnadurai V, Bharathivelan K. Cubic Ideals in Near Subtraction Semigroups. Int J Mod Sci Technol 2016;1(8):276-82.