1.and: Not necessary
Let "G=\\R" then "(G,+)" is a group.
But multiplication is also a binary operation on "G."
2.Ans: Not necessary
Counter example 1.
Let "G=\\frac{Q}{\\Z}" Then elements of "G" are looks like "\\frac{p}{q}+\\Z" ,whose order is "q" . But the order of the group is not finite.
Counter example 2.
Let "G=" "\\Z_2\u00d7\\Z_2\u00d7............" up to infinity time.
Then G is an infinite group but order of each elements is finite.
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