In Z, find all generators of the subgroup <10>  <12>.

Find two groups of order 6 that are not isomorphic.

Find all generators of Z6, Z8, and Z20.

Let Zodd represent the set of odd integers, {... -5, -3, -1, 1, 3, 5, ...}. Determine if the system (Zodd, +): (i) is closed; (ii) is associative; (iii) has an identity element; (iv) has inverses; and (v) is commutative. Is (Zodd, +) a semi-group?  Explain Is (Zodd, +) a group?  Explain

Find all the elements of a factor group Z3X Z4 /

Find all the producers and subgroups of the (Z10, +) group.

In point group D2d, for each of the irreducible representations, verify that the sum of the squares of the characters equals the order of the group.

Let Zeven represent the set of even integers, {... -6, -4, -2, 0, 2, 4, 6, ...}. Determine if the system (Zeven, +): (i) is closed; (ii) is associative; (iii) has an identity element; (iv) has inverses; and (v) is commutative. Is (Zeven, +) a semi-group?  Explain Is (Zeven, +) a group?  Explain

find the domain and codomain of the transformation def ined by the equations.

Find (a) ATA and (b) AAT. Show that each of these products is symmetric.