For $|G|=m$ and random $x_1, dots, x_min G$, (dis)prove that $prod x_i$ is uniformly distributed over the...
For $|G|=m$ and random $x_1, dots, x_min G$, (dis)prove that $prod x_i$ is uniformly distributed over the elements of $G$.
probability group-theory finite-groups uniform-distribution
edited Nov 28 '18 at 19:03
Shaun
8,805113680
asked Mar 3 '14 at 22:10
Jonathan Aronson
408210
add a comment |
For $|G|=m$ and random $x_1, dots, x_min G$, (dis)prove that $prod x_i$ is uniformly distributed over the elements of $G$.
probability group-theory finite-groups uniform-distribution
edited Nov 28 '18 at 19:03
Shaun
8,805113680
asked Mar 3 '14 at 22:10
Jonathan Aronson
408210
add a comment |
For $|G|=m$ and random $x_1, dots, x_min G$, (dis)prove that $prod x_i$ is uniformly distributed over the elements of $G$.
probability group-theory finite-groups uniform-distribution
edited Nov 28 '18 at 19:03
Shaun
8,805113680
asked Mar 3 '14 at 22:10
Jonathan Aronson
408210
For $|G|=m$ and random $x_1, dots, x_min G$, (dis)prove that $prod x_i$ is uniformly distributed over the elements of $G$.
probability group-theory finite-groups uniform-distribution
probability group-theory finite-groups uniform-distribution
edited Nov 28 '18 at 19:03
Shaun
8,805113680
asked Mar 3 '14 at 22:10
Jonathan Aronson
408210
edited Nov 28 '18 at 19:03
Shaun
8,805113680
asked Mar 3 '14 at 22:10
Jonathan Aronson
408210
edited Nov 28 '18 at 19:03
Shaun
8,805113680
edited Nov 28 '18 at 19:03
Shaun
8,805113680
edited Nov 28 '18 at 19:03
Shaun
8,805113680
8,805113680
asked Mar 3 '14 at 22:10
Jonathan Aronson
408210
asked Mar 3 '14 at 22:10
Jonathan Aronson
408210
asked Mar 3 '14 at 22:10
Jonathan Aronson
408210
408210
add a comment |
add a comment |
1 Answer
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Let $G = {g_1, g_2, ldots, g_m}$, and let $g in G$. The key is that $G = {gg_1, gg_2, ldots, gg_m}$. First write down an $m times m$ matrix of all possible products of pairs $g,h in G$. What do you notice? How can you continue until you have written down all possible products of $m$-tuples?
answered Mar 3 '14 at 22:26
Andrew Kelley
1,184424
add a comment |
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1 Answer
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1 Answer
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Let $G = {g_1, g_2, ldots, g_m}$, and let $g in G$. The key is that $G = {gg_1, gg_2, ldots, gg_m}$. First write down an $m times m$ matrix of all possible products of pairs $g,h in G$. What do you notice? How can you continue until you have written down all possible products of $m$-tuples?
answered Mar 3 '14 at 22:26
Andrew Kelley
1,184424
add a comment |
Let $G = {g_1, g_2, ldots, g_m}$, and let $g in G$. The key is that $G = {gg_1, gg_2, ldots, gg_m}$. First write down an $m times m$ matrix of all possible products of pairs $g,h in G$. What do you notice? How can you continue until you have written down all possible products of $m$-tuples?
answered Mar 3 '14 at 22:26
Andrew Kelley
1,184424
add a comment |
Let $G = {g_1, g_2, ldots, g_m}$, and let $g in G$. The key is that $G = {gg_1, gg_2, ldots, gg_m}$. First write down an $m times m$ matrix of all possible products of pairs $g,h in G$. What do you notice? How can you continue until you have written down all possible products of $m$-tuples?
answered Mar 3 '14 at 22:26
Andrew Kelley
1,184424
Let $G = {g_1, g_2, ldots, g_m}$, and let $g in G$. The key is that $G = {gg_1, gg_2, ldots, gg_m}$. First write down an $m times m$ matrix of all possible products of pairs $g,h in G$. What do you notice? How can you continue until you have written down all possible products of $m$-tuples?
answered Mar 3 '14 at 22:26
Andrew Kelley
1,184424
answered Mar 3 '14 at 22:26
Andrew Kelley
1,184424
answered Mar 3 '14 at 22:26
Andrew Kelley
1,184424
answered Mar 3 '14 at 22:26
Andrew Kelley
1,184424
1,184424
add a comment |
add a comment |
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