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problem:examples_of_abstract_groups
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problem:examples_of_abstract_groups [2013/08/21 09:40] joshuawiscons created |
problem:examples_of_abstract_groups [2013/08/21 09:50] (current) joshuawiscons [External links] |
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| ====== Examples Of Abstract Groups ====== | ====== Examples Of Abstract Groups ====== | ||
| ==== Problem ==== | ==== Problem ==== | ||
| - | Give examples of groups with the following properties. Feel free to make them as simple as possible. | + | Give examples of [[definition: |
| - | - A finite abelian group | + | - A finite |
| - | - A finite nonabelian group | + | - A finite |
| - | - A finite group with exactly one proper nontrivial subgroup | + | - A finite |
| - | - An infinite abelian group | + | - An infinite |
| - | - An infinite nonabelian group | + | - An infinite |
| - | - An infinite group in which no nontrivial element has finite order | + | - An infinite |
| - | - An infinite group in which every element has finite order | + | - An infinite |
| - | - An infinite group with exactly one nontrivial element of finite order | + | - An infinite |
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| Line 41: | Line 41: | ||
| * None. | * None. | ||
| - | {{tag> | + | {{tag> |
problem/examples_of_abstract_groups.1377092455.txt.gz · Last modified: 2013/08/21 09:40 by joshuawiscons
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