#13726: The semimonomial group
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Reporter: tfeulner | Owner: joyner
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.6
Component: group theory | Keywords: (semi-)monomial group,
semilinear action, isometry group
Work issues: | Report Upstream: N/A
Reviewers: | Authors: Thomas Feulner
Merged in: | Dependencies:
Stopgaps: |
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A semimonomial group over a ring `R` of length `n` is equal to the wreath
product of the monomial group and the group of ring automorphisms. The
multiplication of two elements `(\phi, \pi, \alpha)(\psi, \sigma, \beta)`
with
* `\phi, \psi \in {R^*}^n`
* `\pi, \sigma \in S_n`
* `\alpha, \beta \in Aut(R)`
is defined by:
`(\phi, \pi, \alpha)(\psi, \sigma, \beta) := (\phi * \psi^{\pi,
\alpha}, \pi * \sigma, \alpha * \beta)`
with
`\psi^{\pi, \alpha} := (\alpha^{-1}(\psi_{\pi(0} ) ), \ldots,
\alpha^{-1}(\psi_{\pi(n-1} ) ) )`
and an elementwisely defined multiplication of vectors.
This group plays an important role in coding theory since it is the group
of all semilinear isometries (relative to the Hamming/Lee/homogenous
metric) of the ambient space.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13726>
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