The seventh and eight Lie dimension subgroups

It is proved that, for any group G, the nth Lie dimension subgroup D( n )( G) coincides with the nth lower central subgroup γ n ( G) for n = 7 and n = 8. Together with the earlier known results for n≤6 (due to Sandling) and n≥9 (due to Hurley and Sehgal), this completely resolves the Lie dimension s...

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Bibliographic Details
Published inJournal of pure and applied algebra Vol. 88; no. 1; pp. 107 - 117
Main Authors Gupta, Narain, Tahara, Ken-Ichi
Format Journal Article
LanguageEnglish
Published Elsevier B.V 25.08.1993
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Summary:It is proved that, for any group G, the nth Lie dimension subgroup D( n )( G) coincides with the nth lower central subgroup γ n ( G) for n = 7 and n = 8. Together with the earlier known results for n≤6 (due to Sandling) and n≥9 (due to Hurley and Sehgal), this completely resolves the Lie dimension subgroup conjecture.
ISSN:0022-4049
1873-1376
DOI:10.1016/0022-4049(93)90016-M