All Questions
6 questions
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How to Construct a Larger Set of Generators for Sp(2n, q) to Optimize Diameter? [closed]
For the symplectic group Sp(2n, q) over a finite field of order q, I am interested in constructing a set of generators that produces a Cayley graph with a "good diameter." Specifically:
By &...
- 19
3
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1
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123
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The rank of Sylow subgroup of special linear groups over finite fields
Let $p,\ell$ be two primes, and let $\mathbb{F}_{q}$ be a finite field of order $q=p^r$. We define the rank of a finite group $G$ to the smallest cardinality of a generating set for $G$. We denote by $...
- 585
2
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0
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Order of $PSL(n,q)$
Being $F$ the field of order $q$ that linear groups are defined here, there is something I can't understand.
I know that $|SL(n,q)| = \dfrac{|GL(n,q)|}{(q-1)}$, and I know that $PSL(n,q) = SL(n,q)/Z(...
- 515
2
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0
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506
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Generators of $SL_2 (F_q)$
I am working on the following problem.
Let $\mathbb{F}_q$ be a finite field with $q \neq 9$ elements and $a$ be a generator of the cyclic group $\mathbb{F}_q^{\times}$. Show that $\mathrm{SL}_2(\...
- 71
2
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277
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Generators and commutator Subgroup of $SL(2,3)$
I'm studying about the special linear group and having some problem about the group $G=SL(2,3)$ (the same denote with $SL(2,\mathbb{F}_3)$:
How can i compuse the generators $\{X,Y\}$ of $G$ with the ...
- 343
2
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1
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361
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Exercise 4.7.8 Dixon-Mortimer "Permutation groups".
Suppose that $m$>$1$ is an integer, and $p$ and $r$ are primes such that $r$
divides $p^{m}-1$ but $r$ does not divide $p^k-1$ for $1$$\leq$ $k$ <$m$. Show that $GL_m$$($$p$$)$ has an irreducible ...
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