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- W3085655953 abstract "Abstract Assume G is a finite p -group. We prove that if all <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msub> <m:mi mathvariant=script>𝒜</m:mi> <m:mn>2</m:mn> </m:msub> </m:math> {mathcal{A}_{2}} -subgroups of G are generated by two elements, then so are all non-abelian subgroups of G . By using this result, we classify the p -groups which have at least two <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msub> <m:mi mathvariant=script>𝒜</m:mi> <m:mn>1</m:mn> </m:msub> </m:math> {mathcal{A}_{1}} -subgroups and in which the intersection of every pair of distinct <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msub> <m:mi mathvariant=script>𝒜</m:mi> <m:mn>1</m:mn> </m:msub> </m:math> {mathcal{A}_{1}} -subgroups equals the intersection of all the <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msub> <m:mi mathvariant=script>𝒜</m:mi> <m:mn>1</m:mn> </m:msub> </m:math> {mathcal{A}_{1}} -subgroups. It turns out that such p -groups are the finite p -groups all of whose non-abelian subgroups are generated by two elements, and the converse also almost holds." @default.
- W3085655953 created "2020-09-21" @default.
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- W3085655953 date "2020-09-09" @default.
- W3085655953 modified "2023-10-09" @default.
- W3085655953 title "Finite 𝑝-groups all of whose 𝓐<sub>2</sub>-subgroups are generated by two elements" @default.
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- W3085655953 doi "https://doi.org/10.1515/jgth-2019-0159" @default.
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