#13726: The semimonomial group
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Reporter: tfeulner | Owner: joyner
Type: enhancement | Status:
Priority: major | needs_review
Component: group theory | Milestone: sage-5.13
Keywords: (semi-)monomial group, | Resolution:
semilinear action, isometry group | Merged in:
Authors: Thomas Feulner | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by tfeulner):
Replying to [comment:9 vbraun]:
I made all the changes you suggested except for renaming the group.
> * Is `SemimonomialGroup` really used in the literature? A quick googling
doesn't find any other references. Its a bit confusing since you are not
talking about a generalization of monomial groups. The latter is already
quite general, e.g. every supersolvable group. Perhaps
`AutomorphismGroupOfLinearCode` would be a more fitting description? Or is
there another characterization? I realize that thats a handful, but it
could be made available as `LinearCode.AutomorphismGroup`, say.
There are a few other references, for example T. Honold and I. Landjev:
Linear codes over finite chain rings. But mostly, people do either
restrict themselves to linear isometries, which leads to the action of the
monomial group or they don't express the equivalence relation with the
help of a group action (semilinearly equivalent codes).
I do not understand the rest of your comment. This group '''is''' a
generalization of the monomial group, since you just add the group of
field automorphisms, similar to the construction of the general semilinear
group. I think `AutomorphismGroupOfLinearCode` would be confusing, since
the elements of this group need not to define an automorphism of a linear
code. The automorphism group of a linear code is a subgroup of the
semimonomial group.
Another characterization would be the group of semilinear Hamming
isometries.
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Ticket URL: <http://trac.sagemath.org/ticket/13726#comment:10>
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