DP Further Mathematics HL Questionbank
4.12
Description
[N/A]Directly related questions
- 15M.2.hl.TZ0.9d: Show that if \(S\) is a subgroup of \(G\), then \(f(S)\) is a subgroup of \(H\).
- 15M.2.hl.TZ0.9c: Show that if \(G\) is Abelian, then \(H\) must also be Abelian.
- 15M.2.hl.TZ0.9b: Show that if \(x\) is an element of \(G\), then \(f({x^{ - 1}}) = {\left( {f(x)} \right)^{ - 1}}\).
- 15M.2.hl.TZ0.9a: Show that if \(e\) is the identity in \(G\), then \(f(e)\) is the identity in \(H\).
- 11M.2.hl.TZ0.6c: \(H\) is a group and the function \(\Phi :H \to H\) is defined by \(\Phi (a) = {a^{ - 1}}\) ,...
- 09M.2.hl.TZ0.2A.b: Using Cayley tables or otherwise, show that \(G\) and...
- 07M.1.hl.TZ0.3b: Show that \(\left\{ {S, \times } \right\}\) is isomorphic to the group of complex numbers...
- 12M.1.hl.TZ0.1b: Now consider the group \(\left\{ {{{\rm{S}}_1},{ \times _{20}}} \right\}\) where...
- SPNone.1.hl.TZ0.6: The group \(\left\{ {G, + } \right\}\) is defined by the operation of addition on the set...
- 14M.2.hl.TZ0.2a: The set \(S\) contains the eighth roots of unity given by...
Sub sections and their related questions
Definition of a group homomorphism.
- 15M.2.hl.TZ0.9a: Show that if \(e\) is the identity in \(G\), then \(f(e)\) is the identity in \(H\).
- 15M.2.hl.TZ0.9c: Show that if \(G\) is Abelian, then \(H\) must also be Abelian.
- 15M.2.hl.TZ0.9d: Show that if \(S\) is a subgroup of \(G\), then \(f(S)\) is a subgroup of \(H\).
Definition of the kernel of a homomorphism.
NoneProof that the kernel and range of a homomorphism are subgroups.
NoneProof of homomorphism properties for identities and inverses.
- 15M.2.hl.TZ0.9a: Show that if \(e\) is the identity in \(G\), then \(f(e)\) is the identity in \(H\).
- 15M.2.hl.TZ0.9b: Show that if \(x\) is an element of \(G\), then \(f({x^{ - 1}}) = {\left( {f(x)} \right)^{ - 1}}\).
Isomorphism of groups.
- 11M.2.hl.TZ0.6c: \(H\) is a group and the function \(\Phi :H \to H\) is defined by \(\Phi (a) = {a^{ - 1}}\) ,...
- 09M.2.hl.TZ0.2A.b: Using Cayley tables or otherwise, show that \(G\) and...
- 07M.1.hl.TZ0.3b: Show that \(\left\{ {S, \times } \right\}\) is isomorphic to the group of complex numbers...
- 12M.1.hl.TZ0.1b: Now consider the group \(\left\{ {{{\rm{S}}_1},{ \times _{20}}} \right\}\) where...
- SPNone.1.hl.TZ0.6: The group \(\left\{ {G, + } \right\}\) is defined by the operation of addition on the set...
- 14M.2.hl.TZ0.2a: The set \(S\) contains the eighth roots of unity given by...
