> i guess the actual issue is that groups.misc.AdditiveCyclic(10) produces a
> ring, not a group, hence the confusion:
>
>         sage: G = groups.misc.AdditiveCyclic(10)
>         sage: G in Groups()
>         False

I really love the fact that groups.misc.AdditiveCyclic(10) is "not a group"

> I am not sure we have to pollute rings with various *_cayley_graph in
> order to work around a wrong pointer lazily introduced in the groups.misc
> catalog (#15369).

Makes sense too. What should it be replaced with?

> confusion. Note that it is currently not used within Sage source code,
> except a single doctest in categories/additive_magmas.py.

heyheyhey, whether or not it is used in Sage's own source code, we
must have a one-liner for a cyclic additive group.

> Also, the distinction between "additive" and "mutiplicative" for groups
> (which by definition have only one law) looks weird. In paricular, we
> could not have a uniform name for the neutral element.

+1

> Just in case, note that for multiplication in rings, you can already do:
>
>         sage: IntegerModRing(10).unit_group().cayley_graph()

Whaaaaaat? Unit group? Is that standard terminology? What's wrong with
`.additive_group()` ? I couldn't have guessed that.

Nathann

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