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单词 TheoremsOfSpecialLinearGroupOverAFiniteField
释义

theorems of special linear group over a finite field


Let 𝔽q be the finite field with q elements, and consider the special linear groupMathworldPlanetmath SL(n,𝔽q) over the field 𝔽q.

  1. 1.

    SL(n,𝔽q) is finite. Furthermore, |SL(n,𝔽q)|=1q-1i=0n-1(qn-qi).

  2. 2.

    SL(n,𝔽q) is a perfect groupMathworldPlanetmath, meaning that [SL(n,𝔽q),SL(n,𝔽q)]=SL(n,𝔽q), where [,] is the commutator bracket with two exceptions: SL(2,𝔽2) and SL(2,𝔽3).

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更新时间:2025/5/4 19:08:51