If G is a group with o(g) < 100 and G has subgroups of order 10 and 25, what is the
order of G?
According to Lagrange's theorem for a finite group , the order of every subgroup of divides the order of . Let be the order of . Then divides and divides . It follows that divides Taking into account that we conclude that
Answer: the order of is 50.
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