On Minimal Non-Soluble Groups, the Normalizer Condition and McLain Groups
We prove that a minimal non-soluble ($MN\mathfrak{S}$ in short) Fitting $p$-group $G$ has a proper subgroup $K$ such that for every proper subgroup $R$ of $G$ containing $K$, we have $N_G(R) > R$. In other words, $G$ satisfies the normalizer condition modulo $K$. We also give a positive answer in...
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| Format: | Article |
| Language: | English |
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Aracne
2017-06-01
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| Series: | Advances in Group Theory and Applications |
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| Online Access: | http://www.advgrouptheory.com/journal/Volumes/3/A.%20Arikan%20-%20On%20minimal%20non-soluble%20groups,%20the%20normalizer%20condition%20and%20McLain%20groups.pdf |