Multiplicative Invariant Fields of Dimension ≤6
The finite subgroups of
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| Main Authors: | , , |
|---|---|
| Format: | eBook Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
2023
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| Series: | Memoirs of the American Mathematical Society |
| Subjects: | |
| ISBN: | 9781470460228, 147046022X |
| ISSN: | 0065-9266, 1947-6221 |
| Online Access: | Get full text |
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Table of Contents:
- Introduction -- Preliminaries and the unramified Brauer groups -- CARAT ID of the <inline-formula content-type="math/mathml"> Z \mathbb {Z} </inline-formula>-classes in dimensions <inline-formula content-type="math/mathml"> 5 5 </inline-formula> and <inline-formula content-type="math/mathml"> 6 6 </inline-formula> -- Proof of Theorem -- Classification of elementary abelian groups <inline-formula content-type="math/mathml"> ( C 2 ) k (C_2)^k </inline-formula> in <inline-formula content-type="math/mathml"> G L n ( Z ) GL_n(\mathbb {Z}) </inline-formula> with <inline-formula content-type="math/mathml"> n ≤ 7 n\leq 7 </inline-formula> -- The case <inline-formula content-type="math/mathml"> G = ( C 2 ) 3 G=(C_2)^3 </inline-formula> with <inline-formula content-type="math/mathml"> H u 2 ( G , M ) ≠ 0 H_u^2(G,M)\neq 0 </inline-formula> -- The case <inline-formula content-type="math/mathml"> G = A 6 G=A_6 </inline-formula> with <inline-formula content-type="math/mathml"> H u 2 ( G , M ) ≠ 0 H_u^2(G,M)\neq 0 </inline-formula> and Noether’s problem for <inline-formula content-type="math/mathml"> N ⋊ A 6 N\rtimes A_6 </inline-formula> -- Some lattices of rank <inline-formula content-type="math/mathml"> 2 n + 2 , 4 n 2n+2, 4n </inline-formula>, and <inline-formula content-type="math/mathml"> p ( p − 1 ) p(p-1) </inline-formula> -- GAP computation: an algorithm to compute <inline-formula content-type="math/mathml"> H u 2 ( G , M ) H_u^2(G,M) </inline-formula> -- Tables: multiplicative invariant fields with non-trivial unramified Brauer groups