Talk:Group with operators

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I don't understand the significance of the remark about a group with operators being a mapping from Omega to the set of group endomorphisms. Isn't Omega just a distinguished subset of endomorphisms in the first place so that the mapping is inclusion? Or is there a more general notion of group with operators which is being alluded to? --Michael Kinyon 00:38, 31 July 2006 (UTC)

[edit] stabilizer-like structure

Does somebody know something related to the following structure:

Let E be an R-module, A \subset 2^E, B\subset 2^R, and
E(A,B) = { x\in E | \forall a\in A, \exists b\in B: b x \subset a }

(Note, x is an element, but a,b are subsets of E - sorry for the ascii-limited notation; I wrote 2^E for the power set although I hate this notation.)

It seems like something in-between a stabilizer, radical of a ring, and the von Neumann/Kolmogorov definition of bounded subsets in TVS / modules. I think this should be considered somewhere, but could not find it anywhere. — MFH:Talk 22:03, 12 October 2006 (UTC)