On finite group of small orders
碩士 === 淡江大學 === 數學學系碩士班 === 98 === We study the "semidirect product" of two groups H and K, which is a generalization of the direct product of H and K obtained by relaxing the requirement that both H and K be normal. Semidirect product construction will enable us to build a "...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Others |
| Language: | en_US |
| Published: |
2010
|
| Online Access: | http://ndltd.ncl.edu.tw/handle/47662809493383435426 |
| Summary: | 碩士 === 淡江大學 === 數學學系碩士班 === 98 === We study the "semidirect product" of two groups H and K, which is a generalization of the direct product of H and K obtained by relaxing the requirement that both H and K be normal.
Semidirect product construction will enable us to build a "larger" group from the groups H and K.
If G contains subgroups isomorphic to H and K, in this case the subgroup H will be normal in G but the subgroup K will not necessarily be normal.
Thus, we shall be able to construct non-abelian groups even if H and K are abelian.
|
|---|