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This is how I went about the problem...it may be completely wrong, so please correct me if I am solving the problem in the completely incorrect manner. It made sense in my head though. Here we go... | This is how I went about the problem...it may be completely wrong, so please correct me if I am solving the problem in the completely incorrect manner. It made sense in my head though. Here we go... | ||
| − | Because group G is of order 155 and a and b are non identity elements of different orders in group G, we have | + | Because group G is of order 155 and a and b are non identity elements of different orders in group G, we have: |
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155 = |G| = |a|k_1, for some k_1 > 0 | 155 = |G| = |a|k_1, for some k_1 > 0 | ||
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155 = |G| = |b|k_2, for some k_2 > 0 | 155 = |G| = |b|k_2, for some k_2 > 0 | ||
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Since a and b are non identity elements, |a| /= 1 /= b (not equal...sorry, don't know the code) | Since a and b are non identity elements, |a| /= 1 /= b (not equal...sorry, don't know the code) | ||
Also, since 155 = 31 * 5 and a and b are both of a different order, |a| = k_2 and |b| = k_1, so | Also, since 155 = 31 * 5 and a and b are both of a different order, |a| = k_2 and |b| = k_1, so | ||
Revision as of 11:36, 24 September 2008
This is how I went about the problem...it may be completely wrong, so please correct me if I am solving the problem in the completely incorrect manner. It made sense in my head though. Here we go...
Because group G is of order 155 and a and b are non identity elements of different orders in group G, we have:
155 = |G| = |a|k_1, for some k_1 > 0
155 = |G| = |b|k_2, for some k_2 > 0
Since a and b are non identity elements, |a| /= 1 /= b (not equal...sorry, don't know the code) Also, since 155 = 31 * 5 and a and b are both of a different order, |a| = k_2 and |b| = k_1, so 155 = |a|*|b| = |G|. Thus the only subgroup of G that can contain both a and b is G itself. //
Is this logical?
