FRATTINI SUBGROUP OF THE UNIT GROUP OF CENTRAL SIMPLE ALGEBRAS
2012 ◽
Vol 11
(03)
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pp. 1250061
Keyword(s):
Group A
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Given an F-central simple algebra A = Mn(D), denote by A′ the derived group of its unit group A*. Here, the Frattini subgroup Φ(A*) of A* for various fields F is investigated. For global fields, it is proved that when F is a real global field, then Φ(A*) = Φ(F*)Z(A′), otherwise Φ(A*) = ⋂p∤ deg (A) F*p. Furthermore, it is also shown that Φ(A*) = k* whenever F is either a field of rational functions over a divisible field k or a finitely generated extension of an algebraically closed field k.
2010 ◽
Vol 09
(06)
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pp. 921-932
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1966 ◽
Vol 27
(2)
◽
pp. 625-642
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2017 ◽
Vol 13
(04)
◽
pp. 853-884
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Keyword(s):
2018 ◽
Vol 2018
(745)
◽
pp. 41-58
2018 ◽
Vol 17
(12)
◽
pp. 1850240
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Keyword(s):