The special linear group, SL(n,R), is a normal subgroup of the
general linear subgroup GL(n,R).
Proof: SL(n,R) is the kernel of the determinant function, which
is a group homomorphism. The kernel of a group homomorphism is
always a normal subgroup.
The special linear group, SL(n,R), is a normal subgroup of the
general linear subgroup GL(n,R).
Proof: SL(n,R) is the kernel of the determinant function, which
is a group homomorphism. The kernel of a group homomorphism is
always a normal subgroup.
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The subgroup for class is Order.
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Yes, every subgroup of a cyclic group is cyclic because every
subgroup is a group.
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The properties of a subgroup would include the identity of the
subgroup being the identity of the group and the inverse of an
element of the subgroup would be the same in the group. The
intersection of two subgroups would be a separate group in the
system.
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Species is the lowest subgroup for classifying organisms.