Subgroups, Lagrange’s Theorem, Cyclic Groups
Consider a group G of order p, where p is a prime integer. Suppose for the moment that our conjecture in section 2.3 that ‘the order of an element of a finite group divides the order of the group’ has been proved. There are p elements in G so there exists g ∈ G with g ≠ e. Because G is finite, g has finite order, say r > 1. Moreover by the above supposition r divides p. Now p is prime and r > 1. Hence r = p.
Unable to display preview. Download preview PDF.