Finite Groups of Order <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <msup> <mrow> <mi>p</mi> </mrow> <mrow> <mn>2</mn>
Finite Groups of Order <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1">
<msup>
<mrow>
<mi>p</mi>
</mrow>
<mrow>
<mn>2</mn>
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有限阶群 <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <msup> <mrow> <mi>p</mi> </mrow> <
DOI：
10.1155/2022/2294627
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发表时间：
2022
影响因子：
1.4
通讯作者：
L. Xu
中科院分区：
文献类型：
--
作者：
Qingliang Zhang;L. Xu
< jat: p > < jat: inline-formula >
<jats:p>Let <jats:inline-formula>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="M3">
<mi>G</mi>
</math>
</jats:inline-formula> be a finite group. We know that the order of <jats:inline-formula>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="M4">
<mi>G</mi>
</math>
</jats:inline-formula> and the number of elements of maximal order in <jats:inline-formula>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="M5">
<mi>G</mi>
</math>
</jats:inline-formula> are closely related to the structure of <jats:inline-formula>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="M6">
<mi>G</mi>
</math>
</jats:inline-formula>. This topic involves Thompson’s conjecture. In this paper, we classify the finite groups of order <jats:inline-formula>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="M7">
<msup>
<mrow>
<mi>p</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msup>
<mi>q</mi>
<mi>r</mi>
</math>
</jats:inline-formula> in which the number of elements of maximal order is <jats:inline-formula>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="M8">
<msup>
<mrow>
<mi>p</mi>
</mrow>
<mrow>
<mn>3</mn>
</mrow>
</msup>
<mi>q</mi>
</math>
</jats:inline-formula>, where <jats:inline-formula>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="M9">
<mi>p</mi>
<mo><</mo>
<mi>q</mi>
<mo><</mo>
<mi>r</mi>
</math>
</jats:inline-formula> are different primes.</jats:p>