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Adjunction of roots to nilpotent groups

Published online by Cambridge University Press:  18 May 2009

R. B. J. T. Allenby
R. B. J. T. Allenby
Affiliation:
University CollegeCardiff
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For any nilpotent group B of class c and any given element h of B generating the subgroup H, Wiegold [1] has shown that if, in addition, [B, H] has exponent pr for some prime p and integer r, then B can be embedded in a nilpotent group G such that G also contains psth root for h(s ≧ 1). In fact, Wiegold has gone further and calculated an upper bound for the class of G in terms of the variables c, p, r, s.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 7 , Issue 3 , January 1966 , pp. 109 - 118
Copyright
Copyright © Glasgow Mathematical Journal Trust 1966

References

REFERENCES

1.Wiegold, J., Adjunction of elements to nilpotent groups, J. London. Math. Soc. 38 (1963), 17–26.CrossRefGoogle Scholar
2.Baumslag, G., Wreath products and p-groups, Proc. Cambridge Philos. Soc. 55 (1959), 224–231.CrossRefGoogle Scholar
3.Liebeck, H., Concerning nilpotent wreath products, Proc. Cambridge Philos. Soc. 58 (1962), 443–451.CrossRefGoogle Scholar
4.Golovin, O. N., Nilpotent products of groups, Mat. Sbornik 27 (69) (1950), 427–454. Amer. Math. Soc. Transl. vol. 2, Ser. 2.2 (1956), 89–115.Google Scholar
5.Kargapolov, M. I., Merzlyakov, Ju. I., Remeslennikov, V. N., Completion of groups, Dokl. Akad. Nauk. S.S.S.R. 134 (1960), 518–520.Google Scholar
6.Wiegold, J., Nilpotent products of groups with amalgamations, Pub. Math. Debrecen 6 (1959) 131–168.CrossRefGoogle Scholar