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On the Kernels of Frobenius Groups | ||
| Journal of Mahani Mathematical Research | ||
| دوره 13، شماره 2 - شماره پیاپی 27، آبان 2024، صفحه 563-569 اصل مقاله (447.75 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2024.23211.1609 | ||
| نویسندگان | ||
| Mohammad Reza Darafsheh* 1؛ Hadiseh Saydi2 | ||
| 1School of Mathematics, Statistics, and Computer Science, College of Science, University of Tehran, Tehran, Iran. | ||
| 2Pure and Applied Analytics, School of Mathematical and Statistical Sciences, North-West University, Mahikeng Campus, Mmabatho, South Africa. | ||
| چکیده | ||
| A Frobenius group is a transitive permutation group on a finite set, such that no non-trivial element fixes more than one point and some non-trivial element fixes a point. Using character theory, it is proved that the Frobenius kernel is a normal subgroup of its Frobenius group. In this paper, we present some group-theoretical proofs that the Frobenius kernel is a subgroup of its Frobenius group under certain conditions. | ||
| کلیدواژه‌ها | ||
| frobenius group؛ frobenius complement؛ frobenius kernel | ||
| مراجع | ||
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[14] Shaw, R. H. (1952). Remarks on a theorem of Frobenius. Proc. Amer. Math. Soc., 3: 970-972.
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[16] Thompson, J. G. (1960). Normal p-complements for nite groups. Mathematische Zeitschrift, 72: 332{354. | ||
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