# Talk:Surjunctive group

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Field:  Algebra

What is ${\displaystyle G^{S}}$ in ${\displaystyle f:G^{S}\to G^{S}}$? -- Taku (talk) 11:07, 10 April 2013 (UTC)

I assume that GS has the usual meaning of the set of all maps from S to G. In which case, of course, it should be SG, as it is Def.3.1.1 and Rem.3.1.2 on page 57 of Ceccherini-Silberstein & Coornaert (2010). Deltahedron (talk) 20:02, 10 April 2013 (UTC)
Ah, I see. (I was thinking of things like elements left invariant by S.) -- Taku (talk) 21:52, 10 April 2013 (UTC)

## "Injunctive" groups

What about groups G such that every surjective cellular automaton on G is injective? Are they called "injunctive" groups? GeoffreyT2000 (talk) 02:15, 2 May 2015 (UTC)

Do any nontrivial examples exist? Rule 90 rules out Z as being such a group, for instance. —David Eppstein (talk) 04:54, 2 May 2015 (UTC)