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With your host… Alan Quebec

With your host… Alan Quebec. The four group axioms. Closure Associativity Identity Inverses. Back. A group with 11 elements is this kind of group. Cyclic. Back. The easiest way to tell if a subset of G is a subgroup. Check that if x, y are elements of H, then so is xy -1. Back.

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With your host… Alan Quebec

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  1. With your host… Alan Quebec

  2. The four group axioms

  3. Closure Associativity Identity Inverses Back

  4. A group with 11 elements is this kind of group

  5. Cyclic Back

  6. The easiest way to tell if a subset of G is a subgroup

  7. Check that if x, y are elements of H, then so is xy-1 Back

  8. Why S5 cannot have a subgroup of order 7

  9. Lagrange’s Theorem Back

  10. There are this many elements of order 13 in C13

  11. 12 (1 has order 1) Back

  12. The difference between Gx and Gx (Not just the names of the terms, but their meanings)

  13. Gx is the orbit containing x; Gx is the stabilizer of x Back

  14. The size of an orbit if G = S4

  15. 4 Back

  16. The number of ways to color the edges of a pentagon red,green, and blue

  17. Back

  18. The number of ways to place colored pie slices into a Trivial Pursuit game piece like the one below, if only the orange and yellow pieces can be used

  19. Back

  20. The number of ways to color the edges of a pentagon red,green, and blue where 2 edges are green and 2 edges are blue

  21. Coefficient of rb2g2 is Back Back

  22. The number of errors that this code can correct for: 00000, 01100, 00111, 11001

  23. 0 (minimum distance is 2) Back

  24. The length of a codeword in the linear code given by the associated matrix

  25. 7 Back

  26. The maximum number of codewords in a code of length 7 that can correct for one error

  27. 16, since Back

  28. The number of codewords in the linear code given by the associated matrix

  29. 24 = 16 Back

  30. This is the smallest linear code that contains the codewords 001, 110

  31. 000, 100, 011, 111 (code must be a group) Back

  32. These three sets are all rings

  33. Back

  34. A ring that is not a field has this distinguishing characteristic

  35. Not all nonzero elements have multiplicative inverses Back

  36. This is an example of an invertible power series where all coefficients are nonzero and the coefficient of is 10

  37. Any matching power series that has a invertible constant term Back

  38. The parity (even or odd) of the permutation (12345)

  39. Even; decomposition into transpositions is (12)(23)(34)(45) Back

  40. The order of the permutation (12)(345)

  41. lcm(2, 3) = 6 Back

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