H. Grundman, T. Smith, Automatic realizability of Galois groups of order 16, Proc. AMS 124 (1996), 2631--2640. Home/Search Document Not in Database Summary Related Articles Check |
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Galois Groups Over Nonrigid Fields - Wenfeng Gao David Self-citation (Smith) (Correct)
....F ( # a) It follows that ker(# 1 ) is a subgroup of D C of order 2 which corresponds to a subfield of K of the form D for some F and ker(# 2 ) is a subgroup of D#C of order 4 which corresponds to a subfield of K of the form C . The existence of both D implies (2) See [GSS] and [GS] for more information on the realizability of D#C as a Galois group. Corollary 3.3. Let K F be a Galois extension with Gal(K F ) D# C. Then K contains a unique quadratic extension of F that imbeds into a cyclic quartic extension contained in K F . This quadratic extension imbeds into two ....
H. Grundman, T. Smith, Automatic realizability of Galois groups of order 16, Proc. AMS 124 (1996), 2631--2640.
Galois Groups Over Nonrigid Fields - Gao, Leep, Minac, Smith Self-citation (Smith) (Correct)
....follows that ker( 1 ) is a subgroup of D fC of order 2 which corresponds to a subfield of K of the form D a;b for some b 2 F and ker( 2 ) is a subgroup of D f C of order 4 which corresponds to a subfield of K of the form C a . The existence of both D a;b and C a implies (2) See [GSS] and [GS] for more information on the realizability of DfC as a Galois group. 8 WENFENG GAO, DAVID B. LEEP, J AN MIN A C, AND TARA L. SMITH Corollary 3.3. Let K=F be a Galois extension with Gal(K=F ) Df C. Then K contains a unique quadratic extension of F that imbeds into a cyclic quartic ....
H. Grundman, T. Smith, Automatic realizability of Galois groups of order 16, Proc. AMS 124, (1996), 2631-2640.
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