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该文讨论了一类2^n阶非交换群——(广义)四元数群Q_{2^n}=〈a,b|a^{2^n-1}=1,b^2=a^{2^{n-2}},{b^{-1}ab=a^{-1}〉(n≥3)的自同构群A(Q_{2^n})与全形H(Q_{2^n}))的置换表示,给出了A(Q_{2^n}))与H(Q_{2^n}))的构造. 相似文献
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《代数通讯》2013,41(2):767-786
Abstract Let Q be a conjugacy closed loop, and N(Q) its nucleus. Then Z(N(Q)) contains all associators of elements of Q. If in addition Q is diassociative (i.e., an extra loop), then all these associators have order 2. If Q is power-associative and |Q| is finite and relatively prime to 6, then Q is a group. If Q is a finite non-associative extra loop, then 16 ∣ |Q|. 相似文献
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Timothy Kohl 《代数通讯》2013,41(10):4290-4304
The holomorph of a group G is Norm B (λ(G)), the normalizer of the left regular representation λ(G) in its group of permutations B = Perm(G). The multiple holomorph of G is the normalizer of the holomorph in B. The multiple holomorph and its quotient by the holomorph encodes a great deal of information about the holomorph itself and about the group λ(G) and its conjugates within the holomorph. We explore the multiple holomorphs of the dihedral groups D n and quaternionic (dicyclic) groups Q n for n ≥ 3. 相似文献
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有限秩的可解群的剩余有限性质 总被引:6,自引:0,他引:6
本文讨论了有限秩的可解群的剩余有限性质,推广了Smelkin等人关于多重循环群的几个同类结果. 相似文献
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