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Sylow's Theorems question |
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| Jun15-05, 09:17 AM | #1 |
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Sylow's Theorems question
Hi
Why must a group of order 98 contain a subgroup of order 7? I would think that Sylow's 1st theorem implies there exists at least one Sylow-7-subgroup of order 49 and at least one Sylow-2-subgroup of order 2 (since 98=2x7x7). Thanks Ray Veldkamp |
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| Jun15-05, 10:28 AM | #2 |
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7 is prime, 7 divides 98, hence by Cauchy's theorem there is an element of order 7. The subgroup generated by this element is of order 7.
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| Jun15-05, 08:18 PM | #3 |
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or because the stronger version of sylows theorems say there is always a subgroup of any prime power order that divides the order of the group, not just the maximal prime power order.
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