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The normalizer property for integral group rings of a class of complete monomial groups. (English) Zbl 1298.16022

The authors, in a series of papers, a recent one is [J. Hai and Z. Li, Commun. Algebra 40, No. 7, 2613-2627 (2012; Zbl 1254.16029)] consider the normalizer property of unit groups of integral group rings. Extending a result of T. Petit Lobão and S. K. Sehgal [Commun. Algebra 31, No. 6, 2971-2983 (2003; Zbl 1039.16034)], they prove that the normalizer property holds for group of units of the integral group ring of \(G=H\wr S_m\), where \(H\) is a finite group with a normal 2-Sylow subgroup and \(S_m\) is the symmetric group on \(m\) letters.

MSC:

16U60 Units, groups of units (associative rings and algebras)
20C05 Group rings of finite groups and their modules (group-theoretic aspects)
16S34 Group rings
20E22 Extensions, wreath products, and other compositions of groups
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References:

[1] Coleman D. B., Proc. Amer. Math. Soc. 5 pp 511– (1964)
[2] DOI: 10.2307/3062112 · Zbl 0990.20002 · doi:10.2307/3062112
[3] DOI: 10.1006/jabr.2001.8760 · Zbl 0993.20017 · doi:10.1006/jabr.2001.8760
[4] DOI: 10.1007/s006050200029 · Zbl 1004.20011 · doi:10.1007/s006050200029
[5] DOI: 10.1016/S0022-4049(00)00167-5 · Zbl 0987.16015 · doi:10.1016/S0022-4049(00)00167-5
[6] Hertweck M., J. Group Theory 12 pp 157– (2008)
[7] DOI: 10.1007/s002090100318 · Zbl 1047.20020 · doi:10.1007/s002090100318
[8] DOI: 10.1016/0022-4049(87)90028-4 · Zbl 0624.20024 · doi:10.1016/0022-4049(87)90028-4
[9] DOI: 10.1081/AGB-120029897 · Zbl 1072.20030 · doi:10.1081/AGB-120029897
[10] DOI: 10.1016/S0021-8693(02)00102-3 · Zbl 1017.16023 · doi:10.1016/S0021-8693(02)00102-3
[11] DOI: 10.1080/00927879908826692 · Zbl 0943.16012 · doi:10.1080/00927879908826692
[12] Li Z., J. Group Theory 15 pp 237– (2012)
[13] DOI: 10.1080/00927871003591975 · Zbl 1219.16038 · doi:10.1080/00927871003591975
[14] Mazur M., Expo. Math. 13 pp 433– (1995)
[15] DOI: 10.1006/jabr.1998.7629 · Zbl 0921.16018 · doi:10.1006/jabr.1998.7629
[16] DOI: 10.1016/S0021-8693(02)00156-4 · Zbl 1017.16024 · doi:10.1016/S0021-8693(02)00156-4
[17] DOI: 10.1081/AGB-120021903 · Zbl 1039.16034 · doi:10.1081/AGB-120021903
[18] Rose J. S., A Course on Group Theory (1978)
[19] Sehgal S. K., Units in Integral Group Rings (1993) · Zbl 0803.16022
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