On the irreducible representations of soluble groups of finite rank

A. V. Tushev

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arXiv · 1208.2390

On the irreducible representations of soluble groups of finite rank

A. V. Tushev

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Abstract

We obtained some sufficient and necessary conditions of existence of faithful irreducible representations of a soluble group $G$ of finite rank over a field $k$. It was shown that the existence of such representations strongly depends on construction of the socle of the group $G$. The situation is especially complicated in the case where the field $k$ is locally finite.

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A. V. Tushev. 2012-08-12. On the irreducible representations of soluble groups of finite rank. https://arxiv.org/abs/1208.2390

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