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Sep 25, 2012 at 16:40 comment added Nick Gill I should have also mentioned the notion of the spectrum' of a group, which is the set of maximal elements in the poset of element orders of the group (ordered by divisibility). I don't know the state of the literature on the spectrum' but I know the term crops up in various places.
Sep 25, 2012 at 13:26 comment added Frieder Ladisch No nilpotent group $\neq 1$ is characterized by $\omega(G)$, and I would be surprised to see a solvable group that is, so maybe Mazurov wanted to say "almost all simple groups"?
Sep 25, 2012 at 10:17 history answered Nick Gill CC BY-SA 3.0