These are notes on the talk on invariant rings of divided powers, given at the Workshop on Invariant Theory, Kingston, Ontario, April 8-19 2002. We give some basic results on these rings, showing in particular that for permutation representations or representations in non-modular characteristic the graded vector space structure is the same as for polynomial rings; finding the symmetric invariants; some results on the GL(n,F) invariants; and showing that finite generation fails in a simple case. We find also that polynomial invariant rings of permutation representations admit divided power algebra structures.
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