%0 Journal Article
%T A new approach to character-free proof for Frobenius theorem
%J AUT Journal of Mathematics and Computing
%I Amirkabir University of Technology
%Z 2783-2449
%A Arfaeezarandi, Seyedeh Fatemeh
%A Shahverdi, Vahid
%D 2023
%\ 02/01/2023
%V 4
%N 1
%P 99-103
%! A new approach to character-free proof for Frobenius theorem
%K Finite group
%K Frobenius group
%K Frobenius Theorem
%R 10.22060/ajmc.2022.21305.1085
%X 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.
%U https://ajmc.aut.ac.ir/article_4863_36ef014a4f85c1bbee9f6f358b602a34.pdf