Steps towards proving the Frobenius theorem without using character theory

	Steps towards proving the Frobenius theorem without using character theory
Journal of New Researches in Mathematics
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 11 تیر 1402
نوع مقاله: علمی مروری
شناسه دیجیتال (DOI): 10.30495/jnrm.2023.70731.2350
نویسندگان
Yaghoub Khodadadi Arpanahi ؛ Ali Iranmanesh
Pure Mathematics Department, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran.
چکیده
A celebrated application of the character theory of finite groups is the theorem of Frobenius on the groups that bear his name. The elegant proof of this theorem was obtained at the beginning of this century. It was then a challenge to find character-free proof of this result. There is no known character-free proof of Frobenius Theorem. Recently Corradi and Horvath have obtained some partial results in this direction. A group G is said to be a Frobenius group if there is a subgroup 1 < H < G such that H ∩ H^g = 1 for all g ∊ G - H. K is defined by ( G – U g ∊ G H^g ) U { 1 }. The theorem of Frobenius say K is a subgroup. The purpose of this article is to prove some stronger results. We hope that this article will stimulate more interest in this problem.
کلیدواژه‌ها
Frobenius Theorem؛ Frobenius Group؛ Involution؛ Hall subgroup

آمار تعداد مشاهده مقاله: 144

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