TY - JOUR
ID - 4863
TI - A new approach to character-free proof for Frobenius theorem
JO - AUT Journal of Mathematics and Computing
JA - AJMC
LA - en
SN - 2783-2449
AU - Arfaeezarandi, Seyedeh Fatemeh
AU - Shahverdi, Vahid
AD - Department of Mathematics, Stony Brook University, Stony Brook, New York, USA
AD - Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden
Y1 - 2023
PY - 2023
VL - 4
IS - 1
SP - 99
EP - 103
KW - Finite group
KW - Frobenius group
KW - Frobenius Theorem
DO - 10.22060/ajmc.2022.21305.1085
N2 - 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.
UR - https://ajmc.aut.ac.ir/article_4863.html
L1 - https://ajmc.aut.ac.ir/article_4863_36ef014a4f85c1bbee9f6f358b602a34.pdf
ER -