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Some Questions on Cyclic, Dihedral and Permutation Groups (10/7)

Some Questions on Cyclic, Dihedral and Permutation Groups (10/7). What is the largest order of an element in Z 10 ? A. 2 B. 5 C. 10 D. 4 E. 8 What is the largest order of an element in D 10 ? A. 2 B. 5 C. 10 D. 20 E. 12 What is the largest order of an element in S 10 ?

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Some Questions on Cyclic, Dihedral and Permutation Groups (10/7)

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  1. Some Questions on Cyclic, Dihedral and Permutation Groups (10/7) • What is the largest order of an element in Z10? • A. 2 B. 5 C. 10 D. 4 E. 8 • What is the largest order of an element in D10? • A. 2 B. 5 C. 10 D. 20 E. 12 • What is the largest order of an element in S10? • A. 10 B. 15 C. 21 D. 30 E. 60 • What is the largest order of an element in A10? • A. 10 B. 15 C. 21 D. 30 E. 60 • S10 has 3628800 elements. What is the largest order of an element in the dihedral group of that same order? • A. 10 B. 800 C. 1814400 D. 3628800 E.

  2. More Questions • How many non-trivial proper subgroups does D3 have? • A. 2 B. 3 C. 4 D. 5 E. 6 • How many non-trivial proper subgroups does S3 have? • A. 2 B. 3 C. 4 D. 5 E. 6 • How many non-trivial proper subgroups does Z20have? • A. 0 B. 3 C. 4 D. 6 E. 10 • How many non-trivial proper subgroups does Z19have? • A. 0 B. 2 C. 3 D.5 E. 6 • How many non-trivial proper subgroups does D7have? • A. 2 B. 7 C. 8 D. 10 E. 14 • How many non-trivial proper subgroups does D8have? • A. 6 B. 8 C. 12 D. 15 E. 18 (Toughy!!)

  3. And some more... • How many subgroups of order 8 does Z14 have? • A. 0 B. 1 C. 2 D. 6 E. 7 • How many subgroups of order 7 does Z14 have? • A. 0 B. 1 C. 2 D. 6 E. 7 • How many elements of order 7 does Z14 have? • A. 0 B. 1 C. 2 D. 6 E. 7 • How many elements of order 6 does S5 have? • A. 0 B. 3 C. 10 D. 20 E. 40 • How many elements of order 6 does A5have? • A. 0 B. 3 C. 10 D. 20 E. 40 • How many subgroups of order 6 does S5 have? • A. 0 B. 3 C. 10 D. 20 E. 40 (Toughy also!)

  4. Assignment for Wednesday • Review everything. Prepare questions. Start thinking about and/or creating your reference sheet. • Test #1 is on Friday!

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