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Null Simplex
Null Simplex
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Say we have a finite group $G$ generated by $\langle g_1,g_2,\ldots ,g_n\rangle$ which is a minimal generating set.

What What information is required from this set in order to determine the whole group?

For cyclic groups, all that is needed is the order of some $g_1$, but for a set generated by two elements, I imagine you need the order of $g_1$, $g_2$, and the order of some combination of the two elements.

The motivation is to better understand Cayley graphs and potentially use these ideas to better understand group extensions.

Say we have a finite group $G$ generated by $\langle g_1,g_2,\ldots ,g_n\rangle$ which is a minimal generating set.

What information is required from this set in order to determine the whole group?

For cyclic groups, all that is needed is the order of some $g_1$, but for a set generated by two elements, I imagine you need the order of $g_1$, $g_2$, and the order of some combination of the two elements.

The motivation is to better understand Cayley graphs and potentially use these ideas to better understand group extensions.

Say we have a finite group $G$ generated by $\langle g_1,g_2,\ldots ,g_n\rangle$ which is a minimal generating set. What information is required from this set in order to determine the whole group?

For cyclic groups, all that is needed is the order of some $g_1$, but for a set generated by two elements, I imagine you need the order of $g_1$, $g_2$, and the order of some combination of the two elements.

The motivation is to better understand Cayley graphs and potentially use these ideas to better understand group extensions.

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Sebastiano
Sebastiano
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Say we have a finite group $G$ generated by $<g_1,g_2,…,g_n>$$\langle g_1,g_2,\ldots ,g_n\rangle$ which is a minimal generating set. What

What information is required from this set in order to determine the whole group? For

For cyclic groups, all that is needed is the order of some $g_1$, but for a set generated by two elements, I imagine you need the order of $g_1$, $g_2$, and the order of some combination of the two elements.

The motivation is to better understand Cayley graphs and potentially use these ideas to better understand group extensions.

Say we have a finite group $G$ generated by $<g_1,g_2,…,g_n>$ which is a minimal generating set. What information is required from this set in order to determine the whole group? For cyclic groups, all that is needed is the order of some $g_1$, but for a set generated by two elements, I imagine you need the order of $g_1$, $g_2$, and the order of some combination of the two elements.

The motivation is to better understand Cayley graphs and potentially use these ideas to better understand group extensions.

Say we have a finite group $G$ generated by $\langle g_1,g_2,\ldots ,g_n\rangle$ which is a minimal generating set.

What information is required from this set in order to determine the whole group?

For cyclic groups, all that is needed is the order of some $g_1$, but for a set generated by two elements, I imagine you need the order of $g_1$, $g_2$, and the order of some combination of the two elements.

The motivation is to better understand Cayley graphs and potentially use these ideas to better understand group extensions.

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Null Simplex
Null Simplex
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Information required to determine a group given a minimal generating set

Say we have a finite group $G$ generated by $<g_1,g_2,…,g_n>$ which is a minimal generating set. What information is required from this set in order to determine the whole group? For cyclic groups, all that is needed is the order of some $g_1$, but for a set generated by two elements, I imagine you need the order of $g_1$, $g_2$, and the order of some combination of the two elements.

The motivation is to better understand Cayley graphs and potentially use these ideas to better understand group extensions.