پیوندهای مفید
آمار
| تعداد نشریات | 8 |
| تعداد شماره‌ها | 427 |
| تعداد مقالات | 5,557 |
| تعداد مشاهده مقاله | 6,708,171 |
| تعداد دریافت فایل اصل مقاله | 5,669,549 |
Some properties of the finite Frobenius groups | ||
| AUT Journal of Mathematics and Computing | ||
| مقاله 6، دوره 4، شماره 1، 2023، صفحه 57-61 اصل مقاله (345.21 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2022.21224.1080 | ||
| نویسنده | ||
| Mohammadreza Darafsheh* | ||
| College of Science, University of Tehran, Iran | ||
| چکیده | ||
| The Frobenius group was defined more than 120 years ago and has been the center of interest for researchers in the field of group theory. This group has two parts, complement and kernel. Proving that the kernel is a normal subgroup has been a challenging problem and several attempts have been done to prove it. In this paper we prove some character theory properties of finite Frobenius groups and also give proofs of normality of the kernel in special cases. | ||
| کلیدواژه‌ها | ||
| Frobenius group؛ Frobenius complement؛ Frobenius kernel؛ Character؛ Permutation character | ||
| مراجع | ||
|
[1] L. Dornhoff, Group representation theory. Part A: Ordinary representation theory, vol. 7 of Pure and Applied Mathematics, Marcel Dekker, Inc., New York, 1971.
[2] W. Feit, On a conjecture of Frobenius, Proc. Amer. Math. Soc., 7 (1956), pp. 177–187.
[3] P. Flavell, A note on Frobenius groups, J. Algebra, 228 (2000), pp. 367–376.
[4] G. Frobenius, Uber aufl¨osbare Gruppen. IV. ¨ , Berl. Ber., 1901 (1901), pp. 1216–1230.
[5] L. C. Grove, Groups and characters, Pure and Applied Mathematics, John Wiley & Sons, Inc., New York, 1997. A Wiley-Interscience Publication.
[6] M. Hall, Jr., The theory of groups, The Macmillan Company, New York, N.Y., 1959.
[7] B. Huppert, Endliche Gruppen. I, Die Grundlehren der mathematischen Wissenschaften, Band 134, SpringerVerlag, Berlin-New York, 1967.
[8] W. Knapp and P. Schmid, A note on Frobenius groups, J. Group Theory, 12 (2009), pp. 393–400.
[9] , Frobenius groups of low rank, Arch. Math. (Basel), 117 (2021), pp. 121–127.
[10] H. Kurzweil and B. Stellmacher, The theory of finite groups, Universitext, Springer-Verlag, New York, 2004. An introduction, Translated from the 1998 German original.
[11] D. Passman, Permutation groups, W. A. Benjamin, Inc., New York-Amsterdam, 1968.
[12] R. H. Shaw, Remark on a theorem of Frobenius, Proc. Amer. Math. Soc., 3 (1952), pp. 970–972.
[13] T. C. Tao, A Fourier-analytic proof of Frobenius’ theorem. https://terrytao.wordpress.com/2013/05/ 24/a-fourier-analytic-proof-of-frobeniuss-theorem/, 2013. | ||
|
آمار تعداد مشاهده مقاله: 1,035 تعداد دریافت فایل اصل مقاله: 815 |
||