IsSubgroup - Maple Help

GroupTheory

 IsSubgroup
 test whether one group is contained in another

 Calling Sequence IsSubgroup( H, G )

Parameters

 H - a group G - a group

Description

 • A group $H$ is a subgroup of a group $G$ if $H$ is contained in $G$ and the binary operation on $H$ is the restriction of the binary operation on $G$ to $H$.
 • The IsSubgroup( H, G ) command tests whether the group H is a subgroup of the group G.  It returns true if H is a subgroup of G, and returns false otherwise.  For some pairs H and G of groups, the value FAIL may be returned if IsSubgroup cannot determine whether H is a subgroup of G.

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $G≔\mathrm{Symm}\left(4\right)$
 ${G}{≔}{{\mathbf{S}}}_{{4}}$ (1)
 > $H≔\mathrm{Alt}\left(4\right)$
 ${H}{≔}{{\mathbf{A}}}_{{4}}$ (2)
 > $\mathrm{IsSubgroup}\left(H,G\right)$
 ${\mathrm{true}}$ (3)
 > $\mathrm{IsSubgroup}\left(\mathrm{Alt}\left(5\right),G\right)$
 ${\mathrm{false}}$ (4)

Compatibility

 • The GroupTheory[IsSubgroup] command was introduced in Maple 17.