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seen Oct 26 at 3:14

Oct
19
comment Can this special amalgamated free product group be trivial group?
@Holt, could you give an explaination why the natural map $G\rightarrow K$ is injective? since in our example, $H=G$, so if you consider the element $\alpha(g)\beta(g)^{-1}\in G$, it is mapped to identity in $G*_{G}G$ under the natural map, but $\alpha(g)\beta(g)^{-1}\in G$ is not necessarily the identity in $G$.
Oct
19
asked Can this special amalgamated free product group be trivial group?
Oct
8
awarded  Commentator
Oct
8
comment homotopic between two maps imply the homotopy between their mapping cone
@Matt, many thanks!
Oct
8
asked homotopic between two maps imply the homotopy between their mapping cone
Sep
26
accepted $S^3$ $\cong$ $D^2\times S^1\bigsqcup_{S^1\times S^1} S^1\times D^2$?
Sep
26
comment $S^3$ $\cong$ $D^2\times S^1\bigsqcup_{S^1\times S^1} S^1\times D^2$?
@jmracek, indeed we glue the boundary using the identity map. And thanks to mention ``Heegaard splitting", I just checked the wiki, link, perhaps it is the same as the standard genus one splitting of $S^3$.
Sep
26
asked $S^3$ $\cong$ $D^2\times S^1\bigsqcup_{S^1\times S^1} S^1\times D^2$?
Sep
11
comment Find the order of a group G from its presentation
@Derek, good suggestion, thanks!
Sep
10
comment Find the order of a group G from its presentation
thanks, I have not used GAP before.
Sep
10
comment Find the order of a group G from its presentation
@ Steve, many thanks!
Sep
10
asked Find the order of a group G from its presentation
Sep
9
awarded  Supporter
Sep
5
awarded  Scholar
Sep
5
comment Find the least interger m such that $S_n$ is embedd into $GL_m(F)$
@Holt, thanks for the detail and reference
Sep
5
accepted Find the least interger m such that $S_n$ is embedd into $GL_m(F)$
Sep
4
comment Find the least interger m such that $S_n$ is embedd into $GL_m(F)$
@Holt, could you give more details?
Sep
4
asked Find the least interger m such that $S_n$ is embedd into $GL_m(F)$
Oct
17
comment counting tuples with restricted condition
it seems that your answer is not right, consider$n=2,m=5,d=4$,only one choice is possible$(z_1,z_2)=(3,1)$
Oct
16
comment counting tuples with restricted condition
Thanks Phira, perhaps this is what I want, although it still needs some calculation. Since I expect a close formula that only involves the given number $n,m,d$ to express the answer.