Action of a Frobenius-like group with fixed-point free kernel

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2014-09-01

Author

Ercan, Gülin

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We call a finite group Frobenius-like if it has a nontrivial nilpotent normal subgroup F possessing a nontrivial complement H such that [F,h] = F for all nonidentity elements h is an element of H. We prove that any irreducible nontrivial FH-module for a Frobenius-like group FH of odd order over an algebraically-closed field has an H-regular direct summand if either F is fixed-point free on V or F acts nontrivially on V and the characteristic of the field is coprime to the order of F. Some consequences of this result are also derived.

Subject Keywords

Algebra and Number Theory

URI

https://hdl.handle.net/11511/38368

Journal

JOURNAL OF GROUP THEORY

DOI

https://doi.org/10.1515/jgt-2014-0002

Collections

Department of Mathematics, Article

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Citation Formats

G. Ercan, “Action of a Frobenius-like group with fixed-point free kernel,” JOURNAL OF GROUP THEORY, pp. 863–873, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/38368.