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Math Help - Sylow's Counting Argument

  1. #1
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    Sylow's Counting Argument

    Hi last one here. Any hints on this is appreciated too

    Let G be a group of order 44. Show using Sylow's counting that G has a normal subgroup of order 11. Use the results to classify all groups of order 44.
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  2. #2
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    By Sylow's first theorem it has a subgroup of order 11, let n be the number of these subgroups then n = 1(mod 11) and n divides 2^2 so n=1. Thus, it must be normal.
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