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Corrigendum to “Brauer characters and normal Sylow p-subgroups” [J. Algebra 503 (2018) 265–276]
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Contents lists available at ScienceDirect
Journal of Algebra www.elsevier.com/locate/jalgebra
Corrigendum
Corrigendum to “Brauer characters and normal Sylow p-subgroups” [J. Algebra 503 (2018) 265–276] Hung P. Tong-Viet Department of Mathematical Sciences, Binghamton University, Binghamton, NY 13902-6000, USA
a r t i c l e
i n f o
Article history: Received 13 March 2018 Available online xxxx Communicated by Gernot Stroth
a b s t r a c t The statements of Claim (1) in the proofs of Theorems 2.6 and 3.3 in [1] are incomplete. In this corrigendum we fix these errors and some other typos. © 2018 Elsevier Inc. All rights reserved.
MSC: primary 20C20 secondary 20C15, 20B15 Keywords: Brauer characters p-parts of character degrees Normal Sylow p-subgroups
In the proof of Theorem 2.6 [1] on page 270, Claim (1) should read “G has a unique minimal normal subgroup N and P N G. Moreover, if N is nonabelian, then CG (N ) = 1.” The last line in the proof of Claim (1) should be replaced by “Therefore, G has a unique minimal normal subgroup N . Assume that N is nonabelian. Since CG (N ) is a normal subgroup of G and does not contain N , N ∩ CG (N ) = 1. Now CG (N ) = 1
DOI of original article: https://doi.org/10.1016/j.jalgebra.2018.02.011. E-mail address: [email protected]. https://doi.org/10.1016/j.jalgebra.2018.03.032 0021-8693/© 2018 Elsevier Inc. All rights reserved.
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H.P. Tong-Viet / Journal of Algebra ••• (••••) •••–•••
as otherwise CG (N ) would possess a minimal normal subgroup of G which is different from N .” The last line in page 270 should be “Since Op (G) = 1, we must have CP (N ) = 1.” On page 274, Claim (1) should read “G has a unique minimal normal subgroup N and P N G. Moreover, if N is nonabelian, then CG (N ) = 1.” The last line in the proof of Claim (1) should be replaced by “It follows that CG (N ) = 1 if N is nonabelian.” The last two labellings on page 274 and 275 should be “(3) N is a p -group.” and “(4) N∼ = S k for some integer k ≥ 1 . . . ” References [1] H.P. Tong-Viet, Brauer characters and normal Sylow p-subgroups, J. Algebra 503 (2018) 265–276.
AID:16653 /ERR
[m1L; v1.235; Prn:11/04/2018; 14:03] P.1 (1-2) Journal of Algebra ••• (••••) •••–•••
Contents lists available at ScienceDirect
Journal of Algebra www.elsevier.com/locate/jalgebra
Corrigendum
Corrigendum to “Brauer characters and normal Sylow p-subgroups” [J. Algebra 503 (2018) 265–276] Hung P. Tong-Viet Department of Mathematical Sciences, Binghamton University, Binghamton, NY 13902-6000, USA
a r t i c l e
i n f o
Article history: Received 13 March 2018 Available online xxxx Communicated by Gernot Stroth
a b s t r a c t The statements of Claim (1) in the proofs of Theorems 2.6 and 3.3 in [1] are incomplete. In this corrigendum we fix these errors and some other typos. © 2018 Elsevier Inc. All rights reserved.
MSC: primary 20C20 secondary 20C15, 20B15 Keywords: Brauer characters p-parts of character degrees Normal Sylow p-subgroups
In the proof of Theorem 2.6 [1] on page 270, Claim (1) should read “G has a unique minimal normal subgroup N and P N G. Moreover, if N is nonabelian, then CG (N ) = 1.” The last line in the proof of Claim (1) should be replaced by “Therefore, G has a unique minimal normal subgroup N . Assume that N is nonabelian. Since CG (N ) is a normal subgroup of G and does not contain N , N ∩ CG (N ) = 1. Now CG (N ) = 1
DOI of original article: https://doi.org/10.1016/j.jalgebra.2018.02.011. E-mail address: [email protected]. https://doi.org/10.1016/j.jalgebra.2018.03.032 0021-8693/© 2018 Elsevier Inc. All rights reserved.
JID:YJABR
AID:16653 /ERR
2
[m1L; v1.235; Prn:11/04/2018; 14:03] P.2 (1-2)
H.P. Tong-Viet / Journal of Algebra ••• (••••) •••–•••
as otherwise CG (N ) would possess a minimal normal subgroup of G which is different from N .” The last line in page 270 should be “Since Op (G) = 1, we must have CP (N ) = 1.” On page 274, Claim (1) should read “G has a unique minimal normal subgroup N and P N G. Moreover, if N is nonabelian, then CG (N ) = 1.” The last line in the proof of Claim (1) should be replaced by “It follows that CG (N ) = 1 if N is nonabelian.” The last two labellings on page 274 and 275 should be “(3) N is a p -group.” and “(4) N∼ = S k for some integer k ≥ 1 . . . ” References [1] H.P. Tong-Viet, Brauer characters and normal Sylow p-subgroups, J. Algebra 503 (2018) 265–276.