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arXiv · 2104.10162

Rewriting Group Products with Transversals

Gabriel Zapata
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Abstract

For any group $G$ with subgroup $H$ and a set of representatives $T$ from the set of cosets $G/H$, we develop a rewriting system from $G$ that bequeaths a product into the set decomposition $T\times H$ of $G$, converting it into a group. In return the rewriting system also describes any product between elements in $G$ in terms of elements from $T$ and $H$, while we gain a new universal group-isomorphism between $G$ and $T\times H$. From this framework, we develop the theory of Diffracted Groups.

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Gabriel Zapata. 2021-04-19. Rewriting Group Products with Transversals. https://arxiv.org/abs/2104.10162

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