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arXiv · 2603.23716

On two Abelian Groups Related to the Galois Top

Helmut Ruhland
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Abstract

In mathematical physics the Galois top, introduced by S. Adlaj, possesses a fixed point on one of two Galois axes through its center of mass. This heavy top has two algebraic motion invariants and an additional transcendental motion-invariant. This third invariant depends on an antiderivative of a variable in the canonical phase space. In this article an abelian semigroup and an abelian group are defined that are related to the application of the Huygens-Steiner theorem to points on the Galois axis of a rigid body. This yields non-linear representations of the one-dimensional, affine, linear (semi)group.

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Helmut Ruhland. 2026-03-24. On two Abelian Groups Related to the Galois Top. https://arxiv.org/abs/2603.23716

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