Return true if and only if the group of Lie type G is finite.
Returns true if the group of Lie type G is abelian.
Returns true if the group of Lie type G is a simple group as an
algebraic group, ie, G has no proper
connected normal subgroups. This is true if, and only if, the underlying root
datum is irreducible. Note that this does not usually mean that
G is simple as an abstract group.
In previous releases of Magma this function was incorrectly called IsIrreducible.
Returns true if the group of Lie type G is simply laced, i.e. its Dynkin diagram
contains no multiple bonds.
Returns true if the group of Lie type G is
semisimple.
IsAdjoint(G) : GrpLie -> BoolElt
Returns true if, and only if, the group of Lie type G is
adjoint(i.e. the
isogeny group is trivial).
Returns true if, and only if, the group of Lie type G is weakly adjoint,i.e. its isogeny group is isomorphic to Zn,
where n is the difference between the rank and the semisimple rank of G.
Note that if G is semisimple then this function is identical to IsAdjoint.
Returns true if, and only if, the group of Lie type G is simply connected(i.e. the isogeny group is equal to the fundamental group, i.e. the coisogeny
group is trivial).
Returns true if, and only if, the group of Lie type G is weakly simply connected, i.e. its coisogeny group is
isomorphic to Zn, where n is the difference between the rank and the semisimple rank of G.
Note that if G is semisimple then this function is identical to IsSimplyConnected.
Returns true if and only if the group of Lie type G is split.
Returns true if and only if the group of Lie type G is twisted.
V2.28, 13 July 2023