assign = name

If given the option assign = x, where x is any name, IdentifySmallGroup will assign the isomorphism mapping $G$ to $H$ to the name x. This isomorphism can be used in the same way as the isomorphisms assigned by AreIsomorphic.

If x already has a value, then it needs to be protected from evaluation using quotation marks.

form = fpgroup or form = permgroup

This option can be used together with the assign option, explained above, in order to specify the form of the group $H$ that is the codomain of the isomorphism to be assigned to the name specified in the assign option.

Specifying form = fpgroup results in the codomain being a finitely presented group. Specifying form = permgroup (the default) results in the codomain being a permutation group. You can equivalently specify the string forms of these values, as form = "fpgroup" or form = "permgroup".

If no assign option is specified, then the form option is ignored.

The command IdentifySmallGroup finds if a group $H$ isomorphic to $G$ occurs in the small groups database. (Currently, that means that the order of the group is at most 511.) If so, it returns the numbers under which $H$ occurs in the database.

The value returned is a sequence of two numbers such that calling SmallGroup with those two numbers as arguments returns the group $H$.  The first number is the order of $G$.

$\mathrm{with}\left(\mathrm{GroupTheory}\right)\:$

$\mathrm{IdentifySmallGroup}\left(\mathrm{PSL}\left(3\,2\right)\right)$

$168,42$

$\mathrm{IdentifySmallGroup}\left(\mathrm{PSL}\left(2\,7\right)\right)$

$168,42$

$\mathrm{g1}≔\mathrm{SmallGroup}\left(96\,7\right)$

$\mathrm{g1}≔\mathrm{<\; a\; permutation\; group\; on\; 96\; letters\; with\; 6\; generators\; >}$

$\mathrm{g2}≔\mathrm{CayleyTableGroup}\left(\mathrm{g1}\right)$

$\mathrm{g2}≔\mathrm{<\; a\; Cayley\; table\; group\; with\; 96\; elements\; >}$

$\mathrm{IdentifySmallGroup}\left(\mathrm{g2}\&comma;\&apos;\mathrm{assign}\&equals;\mathrm{iso}\&apos;\right)$

$96,7$

$\mathrm{Domain}\left(\mathrm{iso}\right)$

$\mathrm{<\; a\; Cayley\; table\; group\; with\; 96\; elements\; >}$

$\mathrm{Codomain}\left(\mathrm{iso}\right)$

$\mathrm{<\; a\; permutation\; group\; on\; 96\; letters\; with\; 6\; generators\; >}$

${\mathrm{infolevel}}_{\mathrm{GroupTheory}}≔3$

${\mathrm{infolevel}}_{\mathrm{GroupTheory}}≔3$

$\mathrm{g3}≔\mathrm{SmallGroup}\left(128\&comma;1607\right)$

$\mathrm{g3}≔\mathrm{<\; a\; permutation\; group\; on\; 128\; letters\; with\; 7\; generators\; >}$

$\mathrm{IdentifySmallGroup}\left(\mathrm{g3}\right)$

$128,1607$

The GroupTheory[IdentifySmallGroup] command was introduced in Maple 17.

For more information on Maple 17 changes, see Updates in Maple 17.