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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Solvable groups having system normalizers of prime order


Author: Gary M. Seitz
Journal: Trans. Amer. Math. Soc. 183 (1973), 165-173
MSC: Primary 20D10
DOI: https://doi.org/10.1090/S0002-9947-1973-0347970-6
MathSciNet review: 0347970
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Abstract: Let G be a solvable group having system normalizer D of prime order. If G has all Sylow groups abelian then we prove that $ l(G) = l({C_G}(D)) + 2$, provided $ l(G) \geq 3$ (here $ l(H)$ denotes the nilpotent length of the solvable group H). We conjecture that the above result is true without the condition on abelian Sylow subgroups. Other special cases of the conjecture are handled.


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DOI: https://doi.org/10.1090/S0002-9947-1973-0347970-6
Keywords: Nilpotent length, system normalizers
Article copyright: © Copyright 1973 American Mathematical Society