Classification of finite groups of order ≤ 200 in terms of solvability
Keywords:
Generalized derivations, Prime rings, Near-rings, Mathematical proofs, CommutativityAbstract
The study of solvable groups has been, and continues to be, the most significant area of work in group theory. Our aim in this work is to classify groups of orderup to 200 in terms of solvability. Our starting point of this classification is to prove that any group with fewer than 60 elements is solvable. Finally, we will show that any group of order up to 200 and not 60, 120, 168, 180 is solvable.
Downloads
References
[1.] I. N. Hersteian, Topics in Algebra, John Weley and Son, Inc (1975).
[2.] V. K. Khanna and S. K. Bhambri, A course in Abstract Algebra, second edition, Vikaspublishin[g house, put, Ltd, New Delhi 2002.
[3.] J. Gordon and L. Martin, Representations and Characters of Groups, Cambridge University Press 1993, Math.J. of Okayama Univ., 46, 1-7, (2004).
[4.] J. N. Salunke and A. R. Gotmare, Converse of Lagrange’s Theorem and Solvable Groups. Bulletin of the Marathwada Mathematical Society vol 10, 1, June 2009 36-42.
[5.] J. G. Thompson and W. Feit, Solvablity of groups of odd order, Pacific Journal of Mathematics, 13 (1963) 775-1029.