Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new subgroup lattice characterization of finite solvable groups   We show that if G is a finite group then no chain of modular elements in its
subgroup lattice L(G) is longer than a chief series. Also, we show that if G is
a nonsolvable finite group then every maximal chain in L(G) has length at least
two more than that of the chief length of G, thereby providing a converse of a
result of J. Kohler. Our results enable us to give a new characterization of
finite solvable groups involving only the combinatorics of subgroup lattices.
Namely, a finite group G is solvable if and only if L(G) contains a maximal
chain X and a chain M consisting entirely of modular elements, such that X and
M have the same length.

12
The categories of this paper are: nucl-th
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The categories of this paper are: eess
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol