Loading...
Please wait, while we are loading the content...
Similar Documents
On New Integral Addition Theorems for Bessel Functions.
| Content Provider | Semantic Scholar |
|---|---|
| Author | Thielman, Henry P. |
| Copyright Year | 1929 |
| Abstract | order 2m. In the latter case each of its Sylow subgroups must be cyclic and G must involve an invariant cyclic subgroup whose order is the direct product of the cyclic group of order 3. 2-1 and an arbitrary cyclic group whose order is prime to 6. Moreover, any such direct product can be extended by an operator of order 2m, which transforms the operators of order 3 in this cyclic group into their inverses but is commutative with each of the other operators contained therein so as to obtain a group which has three cyclic subgroups, when the order of such a subgroup is 2m, into any divisor of the order of the group which is prime to 6, but only one such subgroup when its order is not divisible by 2'. Hence the following theorem: If a group contains no more than three cyclic subgroups of the same order and is not a prime power group nor the direct product of such groups it can be constructed by extending the group which is the direct product of the cyclic group of order 3.2`1 and any cyclic group whose order is prime to 6 by means of an operator of order 2' which has its square in this direct product and transforms into their inverses the operators of order 3 contained therein but is commutative with all its other operators. Miller, Blichfeldt, Dickson, Finite Groups, p. 131, 1916. |
| File Format | PDF HTM / HTML |
| DOI | 10.1073/pnas.15.9.731 |
| Alternate Webpage(s) | http://www.pnas.org/content/15/9/731.full.pdf |
| PubMed reference number | 16577228 |
| Alternate Webpage(s) | https://doi.org/10.1073/pnas.15.9.731 |
| Journal | Medline |
| Volume Number | 15 |
| Issue Number | 9 |
| Journal | Proceedings of the National Academy of Sciences of the United States of America |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
