In mathematics, a subgroup H of a group G is a subset of G which is also a group with respect to the same group operation * defined on G. H contains the identity element of G, is closed with respect to *, and all elements of H have their inverses in H as well.
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Yes, every subgroup of a cyclic group is cyclic because every subgroup is a group.
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.
Mathematics"mathematics" is a plural noun already, the subject is Mathematics!
mathematics
there is no difference between Mathematics and Arithmetic because Arithmetic is a branch of mathematics. there is no difference between Mathematics and Arithmetic because Arithmetic is a branch of mathematics.