Page 77, lines 7-13: A subgroup will often inherit certain properties from the larger group: in particular, subgroups of abelian groups are also abelian, and subgroups of cyclic groups are also cyclic. We saw a number of examples of subgroups. Every nontrivial group has at least two: itself and the trivial subgroup {e} consisting of just the identity element. The dihedral group Dn contains the rotation subgroup Rn, which is isomorphic to the cyclic group Zn.
(I'm about a third of the way through writing an undergraduate textbook in abstract algebra.)
no subject
A subgroup will often inherit certain properties from the larger group: in particular, subgroups of abelian groups are also abelian, and subgroups of cyclic groups are also cyclic. We saw a number of examples of subgroups. Every nontrivial group has at least two: itself and the trivial subgroup {e} consisting of just the identity element. The dihedral group Dn contains the rotation subgroup Rn, which is isomorphic to the cyclic group Zn.
(I'm about a third of the way through writing an undergraduate textbook in abstract algebra.)