Abstract
A finite group \(G\) is said to be a generalized Frobenius group with kernel\(F\), if \(F\) is a proper nontrivial normal subgroup of \(G\) and for every element \(Fx\) of prime order of the quotient group \(G/F\) the coset \(Fx\) of the group \(G\) over \(F\) has only \(p\)-elements for some prime \(p\) depending on \(x\). This article considers generalized Frobenius groups with insoluble kernel. We prove that a quotient group of a generalized Frobenius group over its insoluble kernel is a 2-group.
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Funding
The work of the first two authors is supported by NNSF of China (grant 11771409); the work of the third author is supported by Mathematical Center in Akademgorodok; the work of the fourth and fifth authors is supported by RFBR (grant 19-01-00507).
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MSC2010 numbers: 20E07; 20F50
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Wei, X.B., Guo, W.B., Lytkina, D.V. et al. Solubility of Finite Generalized Frobenius with the Kernel of Odd Index. J. Contemp. Mathemat. Anal. 55, 67–70 (2020). https://doi.org/10.3103/S1068362320010082
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DOI: https://doi.org/10.3103/S1068362320010082