Isomorphisms( P1, P2 )
If the polycyclically or freely presented p-groups P1 and the
polycyclically presented p-group P2 are not isomorphic,
Isomorphisms
returns false
.
Otherwise a record is returned that encodes the isomorphisms from P1 to
P2; its components are
epimorphism
:P1.generators
that defines an
isomorphism from P1 to P2,
generators
:
sizeOutG
:
sizeInnG
:
sizeOutG
:
gap> g:= SolvableGroup( "Q8" );; gap> nonab:= AllTwoGroups( Size, 8, IsAbelian, false ); [ Group( a1, a2, a3 ), Group( a1, a2, a3 ) ] gap> nonab[2].name:= "im";; gap> Isomorphisms( g, nonab[2] ); rec( sizeAutG := 24, sizeInnG := 4, sizeOutG := 6, epimorphism := [ a1, a2, a3 ], generators := [ GroupHomomorphismByImages( im, im, [ a1, a2, a3 ], [ a2, a1, a3 ] ), GroupHomomorphismByImages( im, im, [ a1, a2, a3 ], [ a1*a2, a2, a3 ] ) ] )
(The function IsIsomorphic
tests for isomorphism of p-groups.)
Note: If the component P2.isCompatiblePCentralSeries
is not bound
it is computed using IsCompatiblePCentralSeries
.
GAP 3.4.4