Irreducible representations of certain nilpotent groups of finite rank

2024/11/30 by Tushev, Anatolii V. · 1 citation
Mathematics · #11R27 #16S34 #20C07 #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2412.00398

openalex publication_date 2024/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the paper we study irreducible representations of some nilpotent groups of finite abelian total rank. The main result of the paper states that if a torsion-free minimax group G of nilpotency class 2 admits a faithful irreducible representation φ over a finitely generated field k such that chark ∉ Sp(G) then there exist a subgroup N and an irreducible primitive representation ψ of the subgroup N over k such that the representation φ is induced from ψ and the quotient group N/Kerψ is finitely generated.

Cited by

• On commutative invariants for modules over crossed products of minimax nilpotent linear groups

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