@article {
author = {Arfaeezarandi, Seyedeh Fatemeh and Shahverdi, Vahid},
title = {A new approach to character-free proof for Frobenius theorem},
journal = {AUT Journal of Mathematics and Computing},
volume = {4},
number = {1},
pages = {99-103},
year = {2023},
publisher = {Amirkabir University of Technology},
issn = {2783-2449},
eissn = {2783-2287},
doi = {10.22060/ajmc.2022.21305.1085},
abstract = {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.},
keywords = {Finite group,Frobenius group,Frobenius Theorem},
url = {https://ajmc.aut.ac.ir/article_4863.html},
eprint = {https://ajmc.aut.ac.ir/article_4863_36ef014a4f85c1bbee9f6f358b602a34.pdf}
}