A new approach to character-free proof for Frobenius theorem

	A new approach to character-free proof for Frobenius theorem
AUT Journal of Mathematics and Computing
مقاله 12، دوره 4، شماره 1، 2023، صفحه 99-103 اصل مقاله (330.43 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22060/ajmc.2022.21305.1085
نویسندگان
Seyedeh Fatemeh Arfaeezarandi^* ¹؛ Vahid Shahverdi²
¹Department of Mathematics, Stony Brook University, Stony Brook, New York, USA
²Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden
چکیده
Let G be a Frobenius group. Using character theory, it is proved that the Frobenius kernel of G is a normal subgroup of G, which is well-known as a Frobenius theorem. There is no known character-free proof for Frobenius theorem. In this note, we prove it, by assuming that Frobenius groups are non-simple. Also, we prove that whether K is a subgroup of G or not, Sylow 2-subgroups of G are either cyclic or generalized quaternion group. Also by assuming some additional arithmetical hypothesis on G we prove Frobenius theorem. We should mention that our proof is character-free.
کلیدواژه‌ها
Finite group؛ Frobenius group؛ Frobenius theorem
مراجع

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