Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Landau's Theorem for pi-blocks of pi-separable groups   Slattery has generalized Brauer's theory of p-blocks of finite groups to
pi-blocks of pi-separable groups where pi is a set of primes. In this setting
we show that the order of a defect group of a pi-block B is bounded in terms of
the number of irreducible characters in B. This is a variant of Brauer's
Problem 21 and generalizes K\"ulshammer's corresponding theorem for p-blocks of
p-solvable groups. At the same time, our result generalizes Landau's classical
theorem on the number of conjugacy classes of an arbitrary finite group. The
proof relies on the classification of finite simple groups.

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The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
37
The categories of this paper are: supr-con