| 11. | He also made fundamental contributions to the representation theory of the symmetric and alternating groups.
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| 12. | They alternate groups of stiff, shallow wingbeats with glides.
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| 13. | All perfect alternating groups have perfect double covers.
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| 14. | Arrange twigs into groups and glue them onto frame using glue gun, alternating groups lengthwise and crosswise.
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| 15. | For a concrete example, the alternating group on four points, A _ 4, is solvable but not supersolvable.
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| 16. | Alternating groups sometimes behave as if they were groups of Lie type over the field with one element.
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| 17. | Analogously, the alternating group is a subgroup of index 2 in the symmetric group on " n " letters.
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| 18. | And in fact, the smallest simple non-cyclic group is " A " 5, the alternating group over 5 elements.
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| 19. | This has a center of order 2; the quotient modulo the center is isomorphic to the alternating group A 8.
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| 20. | There is a group of judges and an alternate group called the School of Hard Knocks, which judges each contestant.
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