Groups of order 10: Difference between revisions
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That these are the only two possibilities can be shown via the [[classification of groups of order a product of two distinct primes]]. Since <math>10 = 5 \cdot 2</math> and <math>2 \mid (5 - 1)</math>, the number <math>10</math> falls in the ''two isomorphism classes'' case in that classification. | That these are the only two possibilities can be shown via the [[classification of groups of an order two times a prime]], or more generally the [[classification of groups of order a product of two distinct primes]]. Since <math>10 = 5 \cdot 2</math> and <math>2 \mid (5 - 1)</math>, the number <math>10</math> falls in the ''two isomorphism classes'' case in that classification. | ||
Revision as of 08:48, 5 June 2023
This article gives information about, and links to more details on, groups of order 10
See pages on algebraic structures of order 10 | See pages on groups of a particular order
There are, up to isomorphism, two groups of order 10, indicated in the table below:
| Group | GAP ID (second part) | Abelian? |
|---|---|---|
| dihedral group:D10 | 1 | No |
| cyclic group:Z10 | 2 | Yes |
That these are the only two possibilities can be shown via the classification of groups of an order two times a prime, or more generally the classification of groups of order a product of two distinct primes. Since and , the number falls in the two isomorphism classes case in that classification.
