Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New Lie products for groups and their automorphisms   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 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.

4
The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
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The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio