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<p>A finite group <i>G</i> is called an <i>m</i>-cyclic group if it has <i>m</i> cyclic subgroups. In this paper, we classify finite 14-cyclic groups. These results involve a subclass of finite <i>m</i>-cyclic groups of order <i>n</i> with <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(|\pi (n)|\le 3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">|</mo> <mi>π</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> <mo stretchy="false">|</mo> <mo>≤</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>, where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(|\pi (n)|\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">|</mo> <mi>π</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> <mo stretchy="false">|</mo> </mrow> </math></EquationSource> </InlineEquation> is the number of prime divisors of <i>n</i>.</p>

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A Class of Finite m-Cyclic Groups

  • 期刊论文

  • 发表日期：

    2026年6月15日

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  • Hailin Liu,
  • Zhuhua Shi,
  • Xiangyu Chen

摘要

A finite group G is called an m-cyclic group if it has m cyclic subgroups. In this paper, we classify finite 14-cyclic groups. These results involve a subclass of finite m-cyclic groups of order n with \(|\pi (n)|\le 3\) | π ( n ) | ≤ 3 , where \(|\pi (n)|\) | π ( n ) | is the number of prime divisors of n.