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Implement constructors for the semigroups of all k x k matrices over Z/nZ, for composite n #779

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wilfwilson opened this issue May 20, 2021 · 0 comments
Open

Implement constructors for the semigroups of all k x k matrices over Z/nZ, for composite n #779

wilfwilson opened this issue May 20, 2021 · 0 comments
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help wanted A label for issues where help is wanted. new-feature A label for PRs that contain new features newcomer-friendly A label for issues that are good for first time contributors.

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wilfwilson commented May 20, 2021 •
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By Theorem 5.1.1 in https://arxiv.org/abs/2012.10323, the semigroup of all square matrices of dimension k over Z/nZ is generated by GL(k, Z/nZ) along with one specified matrix for each prime divisor of n.

Generators for GL(k, Zn) can be obtained from GAP via GeneratorsOfGroup(GeneralLinearGroup(k, ZmodnZ(n))); (and are probably easy to deduce anyway - we're not asking for minimality).

The main question is: which ring object should we use for the entries of the matrices? The GAP rings created by ZmodnZ? A Semigroups package semiring? Something else?
@wilfwilson wilfwilson added new-feature A label for PRs that contain new features help wanted A label for issues where help is wanted. newcomer-friendly A label for issues that are good for first time contributors. labels May 20, 2021
@wilfwilson wilfwilson changed the title Implement constructors for the semigroups of all k x k matrices over Z/nZ, for composite n. Implement constructors for the semigroups of all k x k matrices over Z/nZ, for composite n May 20, 2021
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