Largeness of the Set of Finite Products in a Semigroup
نویسندگان
چکیده
We investigate when the set of finite products of distinct terms of a sequence 〈xn〉n=1 in a semigroup (S, ·) is large in any of several standard notions of largeness. These include piecewise syndetic, central , syndetic, central* , and IP*. In the case of a “nice” sequence in (S, ·) = (N,+) one has that FS(〈xn〉n=1) has any or all of the first three properties if and only if {xn+1 − ∑n t=1 xt : n ∈ N} is bounded from above.
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