DP Mathematics HL Questionbank
Cyclic groups.
Description
[N/A]Directly related questions
- 18M.3srg.hl.TZ0.1d: The binary operation multiplication modulo 10, denoted by ×10 , is defined on the set V = {1, 3...
- 18M.3srg.hl.TZ0.1c.ii: Hence show that {T, ×10} is cyclic and write down all its generators.
- 18M.3srg.hl.TZ0.1c.i: Find the order of each element of {T, ×10}.
- 16M.3srg.hl.TZ0.1c: Determine the orders of all the elements of \(\{ S,{\text{ }} * \} \).
- 16N.3srg.hl.TZ0.3b: (i) State a generator for \(\{ H,{\text{ }} * \} \). (ii) Write down the elements of...
- 16N.3srg.hl.TZ0.3a: State the possible orders of an element of \(\{ G,{\text{ }} * \} \) and for each order give an...
- 08M.3srg.hl.TZ1.3: (a) Find the six roots of the equation \({z^6} - 1 = 0\) , giving your answers in the form...
- 08M.3srg.hl.TZ2.1: (a) Draw the Cayley table for the set of integers G = {0, 1, 2, 3, 4, 5} under addition...
- 09M.3srg.hl.TZ0.1: (a) Show that {1, −1, i, −i} forms a group of complex numbers G under multiplication. (b) ...
- 10M.3srg.hl.TZ0.5: Let G be a finite cyclic group. (a) Prove that G is Abelian. (b) Given that a is a...
- 10N.3srg.hl.TZ0.4: Set...
- 14N.3srg.hl.TZ0.4b: Let \(\{ H,{\text{ }} \circ \} \) be the cyclic group of order seven, and let \(p\) be a...
