#13366: Add Semidihedral Groups and Split Metacyclic Groups as Permutation
Groups
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Reporter: khalasz | Owner: joyner
Type: enhancement | Status: needs_review
Priority: minor | Milestone: sage-5.3
Component: group theory | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Kevin Halasz | Merged in:
Dependencies: | Stopgaps:
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Description changed by khalasz:
Old description:
> Adds two new families of groups to Sage's named permgroups database.
> These are two families of p-groups notable for the fact that each group
> contains a cyclic subgroup of index p.
>
> The semidihedral groups are 2-groups which can be thought of as the
> semidirect product of `C_2` with `C_2^{m-1}`, for some m, where `C_2`
> acts on `C_2^{m-1}` by sending elements to their `-1+2^{m-2}` th power.
> It adds new groups, not part of any other family of named permgroups, of
> order `2^m` for each m greater than or equal to 4.
>
> The splitmetcyclic groups are p-groups which can be thought of as the
> semidirect product of `C_p` with `C_p^{m-1}`, for some m, where where
> `C_p` acts on `C_p^{m-1}` by sending elements to their `1+p^{m-2}` th
> power. It adds new groups of order `p^m`, for odd p and m greater than or
> equal to 3, and new groups of order `2^m` for m greater than or equal to
> 4.
>
> '''Apply'''
> 1. [attachments: 13366_groupsfromgorenstein.patch]
New description:
Adds two new families of groups to Sage's named permgroups database.
These are two families of p-groups notable for the fact that each group
contains a cyclic subgroup of index p.
The semidihedral groups are 2-groups which can be thought of as the
semidirect product of `C_2` with `C_2^{m-1}`, for some m, where `C_2` acts
on `C_2^{m-1}` by sending elements to their `-1+2^{m-2}` th power. It adds
new groups, not part of any other family of named permgroups, of order
`2^m` for each m greater than or equal to 4.
The splitmetcyclic groups are p-groups which can be thought of as the
semidirect product of `C_p` with `C_p^{m-1}`, for some m, where where
`C_p` acts on `C_p^{m-1}` by sending elements to their `1+p^{m-2}` th
power. It adds new groups of order `p^m`, for odd p and m greater than or
equal to 3, and new groups of order `2^m` for m greater than or equal to
4.
'''Apply'''
1. [attachment: 13366_groupsfromgorenstein.patch]
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13366#comment:3>
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