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Results tagged with gr.group-theory
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user 64294
Questions about the branch of algebra that deals with groups.
12
votes
1
answer
530
views
Is there an algorithm to decide if a word is in a finitely generated subgroup of a free group?
Let $S$ be a finite set and $F$ is the free group on that set. Is there an algorithm which takes as input a sequence of $w,w_1,\ldots,w_k\in F$ and decides whether $w\in \langle w_1,\ldots,w_k\rang …
- 63.9k
12
votes
0
answers
249
views
What Is The Minimal Monomial of the Symmetric Group?
In the symmetric group $S_n$ what is the shortest sequence $c_1,\ldots,c_k\in S_n$ such that, for all $x\in S_n$ the following product of conjugates of $x$:
$$x^{c_1}x^{c_2}\ldots x^{c_k}$$
equals the …
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