Secrets of Frobenius Group

Document Type : Original Paper

Author

School of mathematics, statistics and computer science, College of Science, University of Theran, Tehran, Iran

Abstract

Abstract: The class of Frobenius groups is the important class of finite

groups. They appear in both the theory of abstract groups as

well as permutation groups and have applications. In this paper

we have some important properties of Frobenius groups and

classify a class of Frobenius groups called ℚ-groups.

Keywords

Main Subjects

References

[1] M. J. Collins, Some infinite Frobenious groups, J. Alg. 131 (1990) 161-165.
[2] K. Corradi and E. Horuath, Steps towards an elemamtary proof of Frobenious’s theorem, Comm. Alg;24 (1996) 2285-2292.[3] M. R. Darafsheh and H. sharifi, Frobenious Q-groups, Arch. Math. 83 (2004) 102 - 105.[4] L. Dorohoff, Group representation theory, Part A Ordinary representation theory, Marcel Dekker, Inc.,New York, 1971.
[5] W. Feit, On the structure of Forbenious group, Canad. J. Math., 9 (1957) 587-596.
[6] F. G. Frobeniiuo, uber auflosbare Gruppen IV, S’ber. Akad. Wiss. Berlin (1901), 1216 – 1230 ; Ges,Abh. III, 189-203.[7] R. Gow, Groups whose characters are rational-valued, J. Alg. 40, 280-299 (1976).[8] D. S. Passman, Permutation groups, W. A. Benjamin, Inc., New York, 1968.
[9] J. G. Thompson, Finite groups with fixed point automorphisms of prime order, proc. Nat. Acad. Sci.U. S. A 45 (1595), 578-581.
Journal of Advanced Mathematical Modeling
Volume 12, Issue 1
April 2022
Pages 62-70

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History

  • Receive Date: 22 October 2021
  • Revise Date: 10 April 2022
  • Accept Date: 14 December 2021

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