DP Mathematics HL Questionbank
The order of a group element.
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...
- 12M.3srg.hl.TZ0.5a: (i) Show that \(gh{g^{ - 1}}\) has order 2 for all \(g \in G\). (ii) Deduce that gh = hg...
- 08M.3srg.hl.TZ1.5: Let \(p = {2^k} + 1,{\text{ }}k \in {\mathbb{Z}^ + }\) be a prime number and let G be the group...
- 11M.3srg.hl.TZ0.1b: (i) Show that {S , \( * \)} is a group. (ii) Find the order of each element of {S ,...
- 09N.3srg.hl.TZ0.5: Let {G , \( * \)} be a finite group of order n and let H be a non-empty subset of G . (a) ...
- 15N.3srg.hl.TZ0.4c: Find the order of each element in \(T\).
- 15N.3srg.hl.TZ0.3d: (i) Find the maximum possible order of an element in \(\{ H,{\text{ }} \circ \} \). (ii) ...
- 15M.3srg.hl.TZ0.1b: (i) State the inverse of each element. (ii) Determine the order of each element.
- 14N.3srg.hl.TZ0.1b: Find the order of each of the elements of the group.
