(up to isomorphism)

(if my latex were better i'd try to put it all on one line, this is a right-split short exact sequence).

if so, is there a "smaller" diagram which conveys the same information?

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- Oct 9th 2011, 04:41 AMDevenoDoes this uniquely determine G?
(up to isomorphism)

(if my latex were better i'd try to put it all on one line, this is a right-split short exact sequence).

if so, is there a "smaller" diagram which conveys the same information? - Oct 9th 2011, 11:08 AMDrexel28Re: Does this uniquely determine G?
- Oct 9th 2011, 12:35 PMNonCommAlgRe: Does this uniquely determine G?
satisfies the conditions too. so is not uniquely determined.

- Oct 9th 2011, 12:36 PMDrexel28Re: Does this uniquely determine G?
- Oct 9th 2011, 01:19 PMDevenoRe: Does this uniquely determine G?
yes i did mean the other composition ( can i claim it was because i was looking at herstein last night? no? ok, i admit it, i'm just stupid).

so...how would i indicate there is no left-split with a picture, to rule out the trivial semi-direct (that is direct) product? - Oct 9th 2011, 01:23 PMDrexel28Re: Does this uniquely determine G?
- Oct 9th 2011, 01:28 PMDevenoRe: Does this uniquely determine G?
correct. what got me thinking about this, is thinking about identifying D4 solely in terms of homomorphisms to and from it (although i admit including the extra information of the short exact sequence is cheating a little) and wondering how well this can be done, for an arbitrary group.