Timeline for Groups GLn(F) and PSLn(F)
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
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| Aug 2, 2018 at 2:15 | review | Close votes | |||
| Aug 9, 2018 at 17:32 | |||||
| Aug 2, 2018 at 1:23 | history | edited | Martin Sleziak |
Removed the deprecated (abstract-algebra) tag - see the tag info: https://mathoverflow.net/tags/abstract-algebra/info (if there are some other suitable tags, choose them instead.)
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| May 2, 2011 at 7:36 | comment | added | Geoff Robinson | "Someone" is correct. A section of a group $G$ is group of the form $H/K$, where $H$ is a subgroup of $G$ and $K$ is a normal subgroup of $H$. A section therefore need be neither a subgroup nor a homomorphic image of $G$ itself."Someone" also correctly identifies the necessary subgroup $H$ and normal subgroup $K$ of $H$ in the case $G = {\rm GL}(n,F).$ The statement in Rose's book is accurate, as long as one has a correct understanding of the meaning of the word "section" in this context. I do not see the relevance of the accepted answer below to the original question. | |
| Mar 25, 2011 at 13:04 | vote | accept | Mikasa | ||
| Mar 25, 2011 at 12:43 | answer | added | Bugs Bunny | timeline score: -1 | |
| Mar 25, 2011 at 12:15 | comment | added | Mikasa | In fact, if it is clear, since PSL_n(F) [n/=2, F an infinite field] is a non-abelian simple group, one can see that the GL_n(F) is a insoluble group. Maybe PGL_n is right instead of PSL_n?? | |
| Mar 25, 2011 at 11:12 | comment | added | Someone | @Babak: SL_n(F) is a subgroup of GL_n(F), and SL_n(F)/Z(SL_n(F)) is isomorphic to PSL_n(F) (with Z denoting the center). | |
| Mar 25, 2011 at 11:10 | comment | added | Someone | @Anton: "In group theory a section of a group G is a group that is (isomorphic to) a quotient group of a subgroup of G." (see en.wikipedia.org/wiki/Section_%28group_theory%29) | |
| Mar 25, 2011 at 9:56 | comment | added | user1688 | What do you mean by section? There is no map from GL_n to PSL_n, only to PGL_n. | |
| Mar 25, 2011 at 9:33 | history | asked | Mikasa | CC BY-SA 2.5 |