Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Blocks of defect of p-solvable groups   Let $p$ be a prime such that $p \geq 5$. Let $G$ be a finite $p$-solvable
group and let $p^a$ be the largest power of $p$ dividing $\chi(1)$ for an
irreducible character $\chi$ of $G$, we show that $|G:F(G)|_p \leq p^{5.5a}$.
Let $G$ be a finite $p$-solvable group with trivial maximal normal solvable
subgroup and we denote $|G|_p=p^n$, then $G$ contains a block of defect less
than or equal to $\lfloor \frac {2n} {3} \rfloor$.

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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat