Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite groups with Frobenius normalizer condition for non-normal primary
  subgroups   A finite group $P$ is said to be \emph{primary} if $|P|=p^{a}$ for some prime
$p$. We say a primary subgroup $P$ of a finite group $G$ satisfies the
\emph{Frobenius normalizer condition} in $G$ if $N_{G}(P)/C_{G}(P)$ is a
$p$-group provided $P$ is $p$-group. In this paper, we determine the structure
of a finite group $G$ in which every non-subnormal primary subgroup satisfies
the Frobenius normalized condition. In particular, we prove that if every
non-normal primary subgroup of $G$ satisfies the Frobenius condition, then
$G/F(G)$ is cyclic and every maximal non-normal nilpotent subgroup $U$ of $G$
with $F(G)U=G$ is a Carter subgroup of $G$.

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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph