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Original Articles

Generalizations of Groups in which Normality Is Transitive

Pages 3242-3252 | Received 17 Apr 2006, Published online: 25 Sep 2007

REFERENCES

  • Agrawal , R. K. ( 1975 ). Finite groups whose subnormal subgroups permute with all Sylow subgroups . Proc. Amer. Math. Soc. 47 : 77 – 83 .
  • Alejandre , M. J. , Ballester-Bolinches , A. , Pedraza-Aguilera , M. C. ( 2001 ). Finite soluble groups with permutable subnormal subgroups . J. Algebra 240 ( 2 ): 705 – 722 .
  • Asaad , M. ( 2004 ). Finite groups in which normality or quasinormality is transitive . Arch. Math. (Basel) 83 ( 4 ): 289 – 296 .
  • Asaad , M. , Heliel , A. A. ( 2001 ). Finite groups in which normality is a transitive relation . Arch. Math. (Basel) 76 ( 5 ): 321 – 325 .
  • Ballester-Bolinches , A. , Esteban-Romero , R. (2001). Sylow permutable subnormal subgroups of finite groups. II. Bull. Austral. Math. Soc. 64(3):479–486.
  • Ballester-Bolinches , A. , Esteban-Romero , R. ( 2002 ). Sylow permutable subnormal subgroups of finite groups . J. Algebra 251 : 727 – 738 .
  • Ballester-Bolinches , A. , Esteban-Romero , R. ( 2003a ). On finite 𝒯-groups . J. Aust. Math. Soc. 75 ( 2 ): 181 – 191 .
  • Ballester-Bolinches , A. , Esteban-Romero , R. ( 2003b ). On finite soluble groups in which Sylow permutability is a transitive relation . Acta Math. Hungar. 101 ( 3 ): 193 – 202 .
  • Ballester-Bolinches , A. , Beidleman , J. C. , Heineken , H. ( 2003a ). Groups in which Sylow subgroups and subnormal subgroups permute . Illinois J. Math. 47 ( 1–2 ): 63 – 69 . Special issue in honor of Reinhold Baer (1902–1979) .
  • Ballester-Bolinches , A. , Beidleman , J. C. , Heineken , H. ( 2003b ). A local approach to certain classes of finite groups . Comm. Algebra 31 ( 12 ): 5931 – 5942 .
  • Ballester-Bolinches , A. , Esteban-Romero , R. , Pedraza-Aguilera , M. C. ( 2005 ). On a class of p-soluble groups . Algebra Colloquium 12 ( 2 ): 263 – 267 .
  • Beidleman , J. , Brewster , B. , Robinson , D. J. S. ( 1999 ). Criteria for permutability to be transitive in finite groups . J. Algebra 222 : 400 – 412 .
  • Bianchi , M. , Mauri , A. G. B. , Herzog , M. , Verardi , L. ( 2000 ). On finite solvable groups in which normality is a transitive relation . J. Group Theory 3 ( 2 ): 147 – 156 .
  • Bryce , R. A. , Cossey , J. ( 1989 ). The Wielandt subgroup of a finite soluble group . J. London Math. Soc. (2) 40 ( 2 ): 244 – 256 .
  • Doerk , K. , Hawkes , T. ( 1992 ). Finite Soluble Groups . de Gruyter Expositions in Mathematics . Vol. 4 . Berlin : Walter de Gruyter & Co.
  • Fransman , A. ( 1991 ). Factorizations of Groups . PhD dissertation . The Netherlands : University of Amsterdam .
  • The GAP Group ( 2002 ). Gap – groups, algorithms, and programming, version 4.3 . (www.gap-system.orgrpar; .
  • Gaschütz , W. ( 1957 ). Gruppen, in denen das normalteilersein transitiv ist . J. Reine Angew. Math. 198 : 87 – 92 .
  • Gorenstein , D. ( 1980 ). Finite Groups. , 2nd ed. New York : Chelsea Publishing Co.
  • Huppert , B. ( 1967 ). Endliche Gruppen. I . Die Grundlehren der Mathematischen Wissenschaften, Band 134 . Berlin : Springer-Verlag .
  • Iwasawa , K. ( 1941 ). Über die endlichen gruppen und die verbände ihrer untergruppen . J. Fac. Sci. Imp. Univ. Tokyo. Sect. I. 4 : 171 – 199 .
  • Kegel , O. ( 1962 ). Sylow-gruppen und subnormalteiler endlicher gruppen . Math. Z. 78 : 205 – 221 .
  • Ore , O. ( 1939 ). Contributions to the theory of groups of finite order . Duke Math. J. 5 : 431 – 460 .
  • Perez , E. R. Jr. , ( 2002 ). A generalization of t-groups . Southeast Asian Bull. Math. 26 ( 1 ): 63 – 69 .
  • Robinson , D. J. S. ( 1968 ). A note on finite groups in which normality is transitive . Proc. Amer. Math. Soc. 19 : 933 – 937 .
  • Robinson , D. J. S. ( 1996 ). A Course in the Theory of Groups. , 2nd ed. Graduate Texts in Mathematics . Vol. 80 . New York : Springer-Verlag .
  • Robinson , D. J. S. ( 2003 ). Finite groups in which normality or permutability is transitive . Advances in Group Theory . Aracne , Rome , pp. 25 – 42 .
  • Schmidt , R. ( 1994 ). Subgroup Lattices of Groups . de Gruyter Expositions in Mathematics . Vol. 14 . Berlin : Walter de Gruyter & Co.
  • van der Waall , R. W. , Fransman , A. ( 1996 ). On products of groups for which normality is a transitive relation on their frattini factor groups . Quaest. Math. 19 ( 1–2 ): 59 – 82 .
  • Zacher , G. ( 1964 ). I gruppi risolubili finiti in cui i sottogruppi di composizione coincidono con i sottogruppi quasi-normali . Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 37 : 150 – 154 .
  • Communicated by M. R. Dixon.

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