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Topic: Sequences and Subgroups (Read 641 times) |
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ecoist
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Sequences and Subgroups
« on: Jun 11th, 2006, 8:02pm » |
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When Hans Zassenhaus was only 18, he wrote a book on group theory which contains the exercise
Let G be a group of order n. Show that, given any sequence x1,...,xn, of elements of G of length n, some consecutive subsequence, xi,...,xj, 1<=i<=j<=n, has product xi...xj equal to the identity of G.
What about the converse?
Let G be a group containing an n-subset H with the property that, for every sequence of elements of H of length n, some consecutive subsequence has product equal to the identity of G. Must H be a subgroup of G?
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