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Results tagged with symmetric-groups
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user 21857
The symmetric group $S_n$ is the group of permutations of the set of integers $\{1,\dots,n\}$. This has $n!$ elements and is generated by the $n-1$ involutions exchanging consecutive integers. The symmetric groups form the simplest family of Coxeter groups.
3
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2 Possible Generalizations of Cayley's Theorem?
I'm wondering about the following 2 generalizations of Cayley's Theorem (every group embeds in a symmetric group). If these are known to be true/false, references would be appreciated.
1) (Weak Versi …
- 1,261
2
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1
answer
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Cyclic Subgroups of the Symmetric Group
If we write a partition $n=k_1+...+k_r$, then we can create a $(k_1,...,k_r)$-cycle in $S_n$ with order equal to the least common multiple of the $k_i$'s. It is clear that every cyclic subgroup will a …
- 1,261