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<p>The capability of a finite <i>p</i>-groups serves as a key factor in its classification. In this study, we leverage the established classification of <i>p</i>-groups with odd prime order <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(p^n\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>p</mi> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation>(where <i>p</i> is an odd prime) that possess a cyclic subgroup of index <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(p^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>p</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> to ascertain the capability of such groups.</p>

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On the capability of groups of order \(p^{n+2}\)

  • 期刊论文

  • 发表日期：

    2026年6月1日

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  • Zhixiu Li

摘要

The capability of a finite p-groups serves as a key factor in its classification. In this study, we leverage the established classification of p-groups with odd prime order \(p^n\) p n (where p is an odd prime) that possess a cyclic subgroup of index \(p^2\) p 2 to ascertain the capability of such groups.