On the properties of the order of a product in a finite abelian group
This paper is based on the article entitled On The Order of a Product in a Finite Abelian Group , by Dieter Jungnickel, which appeared on the Volume 69, February 1996 issue of the Mathematics Magazine. Let a and b be elements of a finite abelian group G and let m and n be the orders of a and b, resp...
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| Main Authors: | , |
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| Format: | text |
| Language: | English |
| Published: |
Animo Repository
1998
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| Subjects: | |
| Online Access: | https://animorepository.dlsu.edu.ph/etd_bachelors/16510 |
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| Institution: | De La Salle University |
| Language: | English |
| Summary: | This paper is based on the article entitled On The Order of a Product in a Finite Abelian Group , by Dieter Jungnickel, which appeared on the Volume 69, February 1996 issue of the Mathematics Magazine.
Let a and b be elements of a finite abelian group G and let m and n be the orders of a and b, respectively. It is common knowledge that the order of ab divides the least common multiple of m and n (lcm[m,n]). Many people make the mistake of assuming that the order of ab equals the lcm[m,n]. We show some counterexamples to this and find some bounds on the order of ab. |
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