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A Note of \({ CP}_{2}\) Groups

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Abstract

A new class \({ CP}_2\) groups of finite groups was characterized by using an inequality of the orders of elements. In this short paper we give a note of \({ CP}_2\) groups since \({ CP}_2\) groups is a subclass of \({ CP}\)(\({ EPPO}\)) groups. Moreover, we discuss the structure of finite p groups contained in \({ CP}_2\) groups.

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References

  1. Berkovich, Y.: Groups of Prime Power Order, vol. 1. Walter de Gruyter, Berlin (2008)

    MATH  Google Scholar 

  2. Brandl, R.: Finite groups all of whose elements are of prime power order. Boll. U. M. I. (5) 18–A, 491–493 (1981)

    MathSciNet  MATH  Google Scholar 

  3. Cheng, K.N., Deaconescu, M., Lang, M.L., Shi, W.J.: Corrigendum and addendum to “classification of finite groups with all elements of prime order”. Proc. Am. Math. Soc. 117, 1205–1207 (1993)

    Article  MATH  Google Scholar 

  4. Deaconescu, M.: Classification of finite groups with all elements of prime order. Proc. Am. Math. Soc. 106, 625–629 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  5. Higman, G.: Finite groups in which every element has prime power order. J. Lond. Math. Soc. 32, 335–342 (1957)

    Article  MathSciNet  MATH  Google Scholar 

  6. Mann, A.: The power structure of \(p\)-groups I. J. Algebra 42, 121–135 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  7. Neumann, B.H.: Groups whose elements have bounded orders. J. Lond. Math. Soc. 12, 195–198 (1937)

    Article  MathSciNet  MATH  Google Scholar 

  8. Shi, W.J., Yang, W.Z.: A new characterization of \(A_5\) and the finite groups in which every non-identity element has prime order. J. Southwest-China Teach. Coll. 1, 36–40 (1984). (in Chinese)

    Google Scholar 

  9. Shi, W.J., Yang, W.Z.: The finite groups all of whose elements are of prime power order. J. Yunnan Educ. Coll. 1, 2–10 (1986). (in Chinese)

    Google Scholar 

  10. Suzuki, M.: On a class of doubly transitive groups. Ann. Math. 75, 105–145 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  11. Tărnăuceanu, M.: Finite groups determined by an inequality of the orders of their elements. Publ. Math. Debrecen 80, 457–463 (2012)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Chongqing University of Arts and Sciences, Chongqing, 402160, People’s Republic of China

    Wujie Shi

  2. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, People’s Republic of China

    Heng Lv

Authors
  1. Wujie Shi
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  2. Heng Lv
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Corresponding author

Correspondence to Wujie Shi.

Additional information

The project is supported by the Natural Science Foundation of China (Nos. 11171364, 11671063, 11471266).

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Shi, W., Lv, H. A Note of \({ CP}_{2}\) Groups. Commun. Math. Stat. 5, 447–451 (2017). https://doi.org/10.1007/s40304-017-0121-x

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  • DOI: https://doi.org/10.1007/s40304-017-0121-x

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