The elements of the quotient group (2/8).) are {} 2- -208,-108,008,108,208,...) 3- (0,1,2,3,...,8) 4- {...,-24,-16, -8,0,8,16,24,...)
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- The elements of the quotient group (4/(8) are 1- {.0 2- (., -2 08,-108,008,10 8,2 08,.) 3- (0,1,2,3, ..,8} 4- {., -24,-16, -8,0,8,16,24,..} 1 0 2 3 O 4 OFind S4/N elements and show that they can be combined into a group. N={e,(23),(234),(243),(12)(34), (123), (132), (134),(13)(24), (142),(143),(14)(23)}The group (Z4 ⨁ Z12)/<(2, 2)> is isomorphic to one of Z8, Z4 ⨁ Z2, orZ2 ⨁ Z2 ⨁ Z2. Determine which one by elimination.
- The order of the element (1,1) + ((4,4)) in the factor group Z,×Z,/((4,4)) is 6. Select one: True FalseTrue or false? Every group of 125 elements has at least 5 elements that commute with every element in the group.3. Suppose that a group G contains elements of orders 1, 2, 3, 4, ..., 8, 9. What is the minimum order of group G? Explain your answer.