DOI QR코드

DOI QR Code

FINITE GROUPS WITH SOME SEMI-p-COVER-AVOIDING OR ss-QUASINORMAL SUBGROUPS

Kong, Qingjun;Guo, Xiuyun

  • Received : 2013.06.11
  • Published : 2014.07.31

Abstract

Suppose that G is a finite group and H is a subgroup of G. H is said to be an ss-quasinormal subgroup of G if there is a subgroup B of G such that G = HB and H permutes with every Sylow subgroup of B; H is said to be semi-p-cover-avoiding in G if there is a chief series 1 = $G_0$ < $G_1$ < ${\cdots}$ < $G_t=G$ of G such that, for every i = 1, 2, ${\ldots}$, t, if $G_i/G_{i-1}$ is a p-chief factor, then H either covers or avoids $G_i/G_{i-1}$. We give the structure of a finite group G in which some subgroups of G with prime-power order are either semi-p-cover-avoiding or ss-quasinormal in G. Some known results are generalized.

Keywords

ss-quasinormal subgroup;semi-p-cover-avoiding subgroup;saturated formation

References

  1. X. Guo, P. Guo, K. P. Shum, On semi cover-avoiding subgroups of finite groups, J. Pure Appl. Algebra 209 (2007), no. 1, 151-158. https://doi.org/10.1016/j.jpaa.2006.05.027
  2. X. Guo and L. Wang, On finite groups with some semi cover-avoiding subgroups, Acta Math. Sin. (Engl. Ser.) 23 (2007), no. 9, 1689-1696. https://doi.org/10.1007/s10114-007-0946-4
  3. B. Huppert and N. Blackburn, Finite Groups. III, Springer-Verlag, Berlin-New York, 1982.
  4. S. Li, Z. Shen, and X. Kong, On ss-quasinormal subgroups of finite subgroups, Comm. Algebra 36 (2008), 4436-4447. https://doi.org/10.1080/00927870802179537
  5. S. Li, Z. Shen, and J. Liu etc, The influence of ss-quasinormality of some subgroups on the structure of finite groups, J. Algebra 319 (2008), no. 10, 4275-4287. https://doi.org/10.1016/j.jalgebra.2008.01.030
  6. S. Qiao and Y. Wang, Finite groups with some semi-p-cover-avoiding or S-quasinormally embedded subgroups, Asian-Eur. J. Math. 2 (2009), no. 4, 667-680. https://doi.org/10.1142/S179355710900056X
  7. H. Wei and Y. Wang, On c*-normality and its properties, J. Group Theory 10 (2007), 211-223.
  8. Y. Fan, X. Guo, and K. P. Shum, Remarks on two generalizations of normality of sub-groups, Chinese Ann. Math. 27A (2006), no. 2, 169-176.