In group theory, the wreath product is a special combination of two groups based on the semidirect product. It is formed by the action of one group on...
12 KB (1,793 words) - 23:18, 18 September 2024
product of sets Direct product of groups Semidirect product Product of group subsets Wreath product Free product Zappa–Szép product (or knit product)...
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product of sets the direct product of groups, and also the semidirect product, knit product and wreath product the free product of groups the product...
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P-group (section Iterated wreath products)
iterated wreath products of cyclic groups of order p are very important examples of p-groups. Denote the cyclic group of order p as W(1), and the wreath product...
21 KB (2,753 words) - 13:08, 25 October 2023
generalizes the semidirect product Holomorph Lie algebra semidirect sum Subdirect product Wreath product Zappa–Szép product Crossed product DS Dummit and RM Foote...
30 KB (4,542 words) - 19:01, 17 October 2024
a product of groups usually refers to a direct product of groups, but may also mean: semidirect product Product of group subsets wreath product free...
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≅ H, wr denotes the wreath product. This is part of the Krull–Schmidt theorem, and holds more generally for finite direct products. It is possible to take...
26 KB (2,932 words) - 23:03, 19 April 2024
\oplus \mathbb {Z} &i=1,2\\0&i>3.\end{array}}\right.} For a group G, the wreath product is an extension 1 → G p → G ≀ Z / p → Z / p → 1. {\displaystyle 1\to...
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+ 1) is the wreath product of Wp(n) and Wp(1). In general, the Sylow p-subgroups of the symmetric group of degree n are a direct product of ai copies...
46 KB (6,130 words) - 06:34, 24 May 2024
\varphi } . ≀ In group theory, G ≀ H {\displaystyle G\wr H} denotes the wreath product of the groups G and H. It is also denoted as G wr H {\displaystyle...
74 KB (9,776 words) - 16:16, 25 October 2024