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arXiv · 1912.05411

On linear version of an elementary group theory result

Mohsen Aliabadi
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Abstract

Given a cyclic group $G$ of order $p^r$, where $p$ is a prime and $r\in\mathbb{N}$. It is well-known that the order of its greatest proper subgroup $\psi(G)$ and the number of its generators $\phi(G)$ satisfy $\psi(G)+\phi(G)=p^r$. In this paper, we give a linear version of this group theory theorem for primitive subspaces in a field extension using tools from field theory and linear algebra. We also discuss partitions of finite fields by using their primitive subspaces.

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Mohsen Aliabadi. 2019-11-27. On linear version of an elementary group theory result. https://arxiv.org/abs/1912.05411

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