Finite groups with $\Bbb P$-subnormal 2-maximal subgroups

A subgroup $H$ of a group $G$ is called $P$ -{\sl subnormal} in $G$ if either $H = G$ or there is a chain of subgroups $H=H_0\subset H_1\subset…\subset H_n=G $s u c h t h a t$ |H_i:H_{i-1}| $i s p r i m e f o r$ 1\le i\le n $. I n t h i s p a p e r w e s t u d y t h e g r o u p s a l l o f w h o s e 2 - m a x i m a l s u b g r o u p s a r e$ \Bbb P$-subnormal.

Finite groups with $P$ -subnormal 2-maximal subgroups

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Finite groups with $P$ -subnormal 2-maximal subgroups

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Finite groups with PP-subnormal 2-maximal subgroups

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Finite groups with PP-subnormal 2-maximal subgroups

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Finite groups with $P$ -subnormal 2-maximal subgroups

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Finite groups with $P$ -subnormal 2-maximal subgroups

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