#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:11 vbraun]:
> Here is what I'm confused about. A monomial group is one where all
characters are induced from linear characters. Although I haven't checked,
it seems very plausible that the group of monomial transformations is a
monomial group.
I did not find any answer to your question. But the wreath product G \wr
S_n is known as the
''complete monomial group''. So, do you think I should call my group
`CompleteSemimonomialGroup` or `SemimonomialTransformationGroup` to
emphasize the difference?
> But I don't think the converse is true. E.g. S_3 is a monomial group
> {{{
> sage: SymmetricGroup(3).is_monomial()
> True
> }}}
> but doesn't seem to be the group of monomial automorphisms of a vector
space (Is this true?).
>
The symmetric group S_n is the group of monomial automorphisms of the
n-dimensional binary vector space.
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Ticket URL: <http://trac.sagemath.org/ticket/13726#comment:12>
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