New Characterizations of p-Supersolubility of Finite Groups

REFERENCES

• Arroyo-Jordá , M. , Arroyo-Jordá , P. , Martinez-Paster , A. , Pérez-Ramos , M. D. ( 2010 ). On finite products of groups and supersolubility . J. Algebra 323 : 2922 – 2934 .
   Web of Science ®Google Scholar
• Asaad , M. ( 1998 ). On maximal subgroups of Sylow subgroups of finite groups . Comm. Algebra 26 ( 11 ): 3647 – 3652 .
   Web of Science ®Google Scholar
• Assad , M. , Heliel , A. A. ( 2001 ). On S-quasinormally embedded subgroups of finite groups . J. Pure Appl. Algebra 165 : 129 – 135 .
   Web of Science ®Google Scholar
• Asaad , M. , Ramadan , M. , Shaalan , A. ( 1991 ). Influence of S-quasinormality on maximal subgroups of Sylow subgroups of fitting subgroups of a finite group . Arch. Math. 56 ( 6 ): 521 – 527 .
   Web of Science ®Google Scholar
• Ballester-Bolinches , A. , Ezquerro , L. M. , Skiba , A. N. ( 2009 ). Subgroups of finite groups with a strong cover-avoidance property . Bull. Aust. Math. Soc. 79 : 499 – 506 .
   Web of Science ®Google Scholar
• Ballester-Bolinches , A. , Guo , X. Y. ( 1999 ). On complemented subgroups of finite groups . Arch. Math. 72 : 161 – 166 .
   Web of Science ®Google Scholar
• Ballester-Bolinches , A. , Pedraza-Aguilera , M. C. ( 1988 ). Sufficient conditions for supersolubility of finite groups . J. Pure Appl. Algebra 127 : 113 – 118 .
   Web of Science ®Google Scholar
• Ballester-Bolinches , A. , Wang , Y. M. , Guo , X. Y. ( 2000 ). c-Supplemnted subgroups of finite groups . Glasg. Math. J. 42 : 383 – 389 .
   Web of Science ®Google Scholar
• Chen , Z. M. ( 1988 ). Inner-Outer-Σ Groups and Minimal Non-Σ Groups . Chongqing : Southwest Normal University Press .
   Google Scholar
• Doerk , K. , Hawkes , T. ( 1992 ). Finite Soluble Groups . Berlin , New York : Walter de Gruyter .
   Google Scholar
• Gorenstein , D. ( 1980 ). Finite Groups . New York : Chelsea Publishing Co .
   Google Scholar
• Guo , W. B. ( 2000 ). The Theory of Classes of Groups . Beijing-New York-Dorlrecht-Boston-London : Science Press-Kluwer Academic Publishers .
   Google Scholar
• Guo , W. B. , Chen , S. ( 2010 ). Weakly c-permutable subgroups of finite groups . J. Algebra 324 : 2369 – 2381 .
   Web of Science ®Google Scholar
• Guo , W. B. , Shum , K. P. , Skiba , A. N. (2007). X-semipermutable subgroups of finite Groups. J. Algebra 315:31–41.
   Web of Science ®Google Scholar
• Guo , W. B. , Shum , K. P. , Skiba , A. N. ( 2005 ). Conditonally permutable subgroups and supersolubility of finite groups . Southeast Asian Bull. Math. 29 : 493 – 510 .
   Google Scholar
• Guo , W. B. , Shum , K. P. , Skiba , A. N. ( 2007 ). X-Quasinormal subgroups . Siberian Math. J. 48 ( 4 ): 593 – 605 .
   Web of Science ®Google Scholar
• Guo , W. B. , Shum , K. P. , Skiba , A. N. ( 2006 ). Criterions of supersolubility for products of supersoluble groups . Publ. Math. Debrecen 68 ( 3–4 ): 433 – 449 .
   Web of Science ®Google Scholar
• Guo , W. B. , Shum , K. P. , Skiba , A. N. ( 2008 ). Schur-Zassenhaus theorem for X-permutable subgroups . Algebra Colloquium 15 ( 2 ): 185 – 192 .
   Web of Science ®Google Scholar
• Guo , W. B. , Shum , K. P. , Skiba , A. N. ( 2003 ). G-covering subgroup systems for the classes of supersoluble and nilpotent groups . Israel J. Math. 138 : 125 – 138 .
   Web of Science ®Google Scholar
• Guo , W. B. , Shum , K. P. , Skiba , A. N. ( 2004 ). G-covering systems of subgroups for classes of p-supersoluble and p-nilpotent finite groups . Siberian Math. J. 45 ( 3 ): 433 – 442 .
   Web of Science ®Google Scholar
• Guo , W. B. , Xie , F. Y. , Li , B. J. ( 2009 ). Some open questions in the theory of generalized permutable subgroups . Sci. China Ser. A: Math. 52 ( 10 ): 2132 – 2144 .
   Google Scholar
• Guo , X. Y. , Shum , K. P. ( 2005 ). Finite p-nilpotent groups with some subgroups c-supplemented . J. Aust. Math. Soc. 78 ( 3 ): 429 – 439 .
   Google Scholar
• Huppert , B. ( 1967 ). Endliche Gruppen I . Heidelberg , New York : Spring-Verlag .
   Google Scholar
• Huppert , B. , Blackburn , N. ( 1982 ). Finite Groups III . Berlin : Springer-Verlag .
   Google Scholar
• Kegel , O. H. ( 1962 ). Sylow-gruppen und subnormalteiler endlicher gruppen . Math. Z. 78 : 205 – 221 .
   Google Scholar
• Li , B. J. , Skiba , A. N. ( 2008 ). New characerizations of finite supersoluble groups . Sci. China Ser. A: Math. 51 ( 1 ): 827 – 841 .
   Google Scholar
• Li , D. Y. , Guo , X. Y. ( 2001 ). On complemented subgroups of finite groups . Chinese Ann. Math. Ser. B 22 ( 2 ): 249 – 254 .
   Web of Science ®Google Scholar
• Li , Y. M. ( 2006 ). G-Covering systems of subgroups for the class of supersoluble groups . Siberian Math. J. 47 ( 3 ): 474 – 480 .
   Web of Science ®Google Scholar
• Li , Y. M. , Wang , Y. M. ( 2004 ). On π-quasinormally embedded subgroups of finite groups . J. Algebra 281 : 109 – 123 .
   Web of Science ®Google Scholar
• Li , Y. M. , Wang , Y. M. ( 2003 ). The influence of S-quasinormality of some subgroups of a finite group . Arch. Math. 81 : 245 – 252 .
   Web of Science ®Google Scholar
• Ore , O. ( 1993 ). Contributions in the theory of groups of finite order . Duke Math. J. 5 : 431 – 460 .
   Google Scholar
• Ramadan , M. ( 1992 ). Influence of normality on maximal subgroups of Sylow subgroups of a finite group . Acta Math. Hung. 59 ( 1–2 ): 107 – 110 .
   Web of Science ®Google Scholar
• Ramadan , M. , Mohamed , M. E. , Heliel , A. A. ( 2005 ). On c-normality of certain subgroups of prime power order of finite groups . Arch. Math. 85 : 203 – 210 .
   Web of Science ®Google Scholar
• Schmid , P. ( 1998 ). Subgroups permutable with all Sylow subgroups . J. Algebra 207 : 285 – 193 .
   Web of Science ®Google Scholar
• Shemetkov , L. A. ( 1978 ). Formations of Finite Groups . Moscow : Nauka, Main Editorial for Physical and Mathematical Literature .
   Google Scholar
• Shemetkov , L. A. , Skiba , A. N. ( 2009 ). On the 𝒳 Φ-hypocentre of finite groups . J. Algebra 322 : 2106 – 2117 .
   Web of Science ®Google Scholar
• Skiba , A. N. ( 2007 ). On weakly s-permutable subgroups of finite groups . J. Algebra 315 : 192 – 209 .
   Web of Science ®Google Scholar
• Srinivasan , S. ( 1980 ). Two sufficient conditions for supersolubility of finite groups . Israel J. Math. 35 ( 3 ): 210 – 214 .
   Web of Science ®Google Scholar
• Wang , Y. M. ( 1996 ). c-Normality of groups and its properties . J. Algebra 180 ( 3 ): 954 – 965 .
   Web of Science ®Google Scholar
• Wang , Y. M. ( 2000 ). Finite groups with some subgroups of Sylow subgroups c-supplemented . J. Algebra 224 : 467 – 478 .
   Web of Science ®Google Scholar
• Wang , Y. M. , Wei , H. Q. (2004). On a problem of Skiba from the Kourovka Notebook. Sci. China Ser. A: Math. 47(1):96–103.
   Google Scholar
• Wang , Y. M. , Wei , H. Q. , Li , Y. M. ( 2002 ). A generalization of Kramer's Theorem and its applications . J. Aust. Math. Soc. 65 : 467 – 475 .
   Web of Science ®Google Scholar
• Wei , H. Q. , Wang , Y. M. , Li , Y. M. ( 2003 ). On c-normal maximal and minimal subgroups of Sylow subgroups of finite groups II . Comm. Algebra 31 ( 10 ): 4807 – 4816 .
   Web of Science ®Google Scholar
• Wei , H. Q. , Wang , Y. M. , Li , Y. M. ( 2004 ). On c-supplemented maximal and minimal subgroups of Sylow subgroups of finite groups . Proc. Amer. Math. Soc. 132 ( 8 ): 2197 – 2204 .
   Web of Science ®Google Scholar
• Communicated by V. A. Artamonov.
   Google Scholar