On the primitive irreducible representations of finitely generated nilpotent groups

Authors

DOI:

https://doi.org/10.15407/dopovidi2021.04.024

Keywords:

nilpotent groups, group rings, primitive representations

Abstract

We develop some tecniques whish allow us to apply the methods of commutative algebra for studing the representations of nilpotent groups. Using these methods, in particular, we show that any irreducible representation of a finitely generated nilpotent group G over a finitely generated field of characteristic zero is induced from a primitive representation of some subgroup of G.

References

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Harper, D. L. (1980). Primitivity in representations of polycyclic groups. Math. Proc. Camb. Philos. Soc., 88, Iss. 1, pp. 15-31. https://doi.org/10.1017/S0305004100057327

Tushev, A. V. (2000). On primitive representations of soluble groups of finite rank. Sb. Math., 191, No. 11, pp. 1707-1748. https://doi.org/10.4213/sm524

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Bourbaki, N. (1998). Elements of mathematics: commutative algebra, Chapters 1-7. London: Springer.

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Published

26.08.2021

How to Cite

Tushev, A. (2021). On the primitive irreducible representations of finitely generated nilpotent groups. Reports of the National Academy of Sciences of Ukraine, (4), 24–27. https://doi.org/10.15407/dopovidi2021.04.024