New Lie products for groups and their automorphisms
Abstract We generalize the common notion of descending and ascending central series. The descending approach determines a naturally graded Lie ring and the ascending version determines a graded module for this ring. We also link derivations of these rings to the automorphisms of a group. This process uncovers new structure in 4/5 of the approximately 11.8 million groups of size at most 1000 and beyond that point pertains to at least a positive logarithmic proportion of all finite groups.
1978 ◽
Vol 19
(2)
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pp. 153-154
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2018 ◽
Vol 11
(2)
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pp. 137-156
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1980 ◽
Vol 70
(6)
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pp. 2097-2101
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2010 ◽
Vol 20
(1)
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pp. 125-176
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Keyword(s):