Covers of Algebraic Curves
Part of the Progress in Mathematics book series (PM, volume 218)
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Let p be a prime number and let G be a finite group. The subgroup p(G) ⊂ G is defined as the group generated by all elements in G having as order a power of p. Equivalent definitions of p(G) are:
p(G) is the smallest normal subgroup such that the factor group G/p(G) has no elements with order p.
p(G) is generated by all the p-Sylow subgroups of G.
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© Springer Science+Business Media New York 2004