1.6.45 Fields, Groups, Rings

Condition: a) a lot \ (g \)-many material numbers in complexity is a group; b) many \ (a \)-many integers are in the \ (r \) normal divider; c) describe the factor-group \ (g / a \), indicating in it a unit, type of reverse element, group operation; d) to prove that the display \ (\ varphi: h \ rightarrow l \), where \ (h- \) a group of integers, multiple 7, in complication, \ (l-z^{28} \) a group of deductions for modest 28 is homomorphism, calculate its core and image. \ (\ varphi (x) = [x] _ {28} \) - the remainder from division by 28. e) Build a factor-group \ (h / \ Operatorname {ker} \ varphi \), indicating the multiplication table.