# Galois module structure of the units modulo $$p^m$$ of cyclic extensions of degree $$p^n$$

@article{Min2022GaloisMS,
title={Galois module structure of the units modulo \$\$p^m\$\$ of cyclic extensions of degree \$\$p^n\$\$},
author={J{\'a}n Min{\'a}{\vc} and Andrew Schultz and John Swallow},
journal={manuscripta mathematica},
year={2022}
}
• Published 27 May 2021
• Mathematics
• manuscripta mathematica
Let p be prime, and n,m ∈ N. When K/F is a cyclic extension of degree p, we determine the Z/pZ[Gal(K/F )]-module structure of K/K m . With at most one exception, each indecomposable summand is cyclic and free over some quotient group of Gal(K/F ). For fixed values of m and n, there are only finitely many possible isomorphism classes for the non-free indecomposable summand. These Galois modules act as parameterizing spaces for solutions to certain inverse Galois problems, and therefore this…
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