Finite Groups with Four Conjugacy Class Sizes

REFERENCES

• Alemany , E. , Beltrán , A. , Felipe , M. J. ( 2009 ). Finite groups with two p-regular conjugacy class lengths II . Bull. Austral. Math. Soc. 79 : 419 – 425 .
   Google Scholar
• Amberg , B. , Kazarin , L. S. ( 2007 ). On the product of a nilpotent group and a group with non-trivial center . J. Algebra. 311 : 69 – 95 .
   Google Scholar
• Aschbacher , M. ( 1986 ). Finite Group Theory . New York : Cambridge University Press .
   Google Scholar
• Baer , R. ( 1953 ). Group elements of primer power index . Trans. Amer. Math. Soc. 75 : 20 – 47 .
   Web of Science ®Google Scholar
• Beltrán , A. , Felipe , M. J. ( 2003 ). Finite groups with two p-regular conjugacy class lengths . Bull. Austral. Math. Soc. 67 : 163 – 169 .
   Web of Science ®Google Scholar
• Beltrán , A. , Felipe , M. J. ( 2004 ). Prime powers as conjugacy class lengths of π-elements . Bull. Austral. Math. Soc. 69 : 317 – 325 .
   Google Scholar
• Beltrán , A. , Felipe , M. J. ( 2006 ). Variations on a theorem by Alan Camina on conjugacy class sizes . J. Algebra 296 : 253 – 266 .
   Google Scholar
• Beltrán , A. , Felipe , M. J. ( 2006 ). Some class size conditions implying solvability of finite groups . J. Group Theory 9 : 787 – 797 .
   Web of Science ®Google Scholar
• Beltrán , A. , Felipe , M. J. ( 2008 ). Structure of finite groups under certain arithmetical conditions on class sizes . J. Algebra 319 : 897 – 910 .
   Web of Science ®Google Scholar
• Bertram , E. A. , Herzog , M. , Mann , A. ( 1990 ). On a graph related to conjugacy classes of groups . Bull. London Math. Soc. 22 : 569 – 575 .
   Web of Science ®Google Scholar
• Camina , A. R. ( 1972 ). Arithmetical conditions on the conjugacy class numbers of a finite group . J. London Math. Soc. 2 : 127 – 132 .
   Google Scholar
• Camina , A. R. ( 1973 ). Conjugacy classes of finite groups and some theorems of N. It⊚ . J. London Math. Soc. 6 : 421 – 426 .
   Google Scholar
• Camina , A. R. ( 1974 ). Finite groups of conjugate rank 2 . Nagoya Math. J. 53 : 47 – 57 .
   Google Scholar
• Camina , A. R. , Camina , R. D. ( 2009 ). Coprime conjugacy class sizes . Asian-Eur. J. Math. 2 : 183 – 190 .
   Google Scholar
• Feit , W. ( 1960 ). A characterization of the simple groups SL(2, 2 m ) . Amer. J. Math. 82 : 281 – 300 .
   Google Scholar
• Fisman , E. , Arad , Z. ( 1987 ). A proof of Szep's conjecture on non-simplicity of certain finite groups . J. Algebra 108 : 340 – 354 .
   Google Scholar
• Huppert , B. ( 1998 ). Character Theory of Finite Groups . De Gruyter Expositions in Mathematics 25 . Berlin : Walter de Gruyter & Co .
   Google Scholar
• Kazarin , S. L. ( 1981 ). On groups with isolated conjugacy classes . Izvestiya Vysshikh Uchebnyckh Zavedeniy Matematika 7 : 40 – 45 .
   Google Scholar
• Kazarin , L. S. ( 1983 ). On the product of finite groups. Dokl. Akad. Nauk 269(3): 528–531 .
   Google Scholar
• It⊚, N. ( 1953 ). On finite groups with given conjugate types I . Nagoya Math. 6 : 17 – 28 .
   Google Scholar
• It⊚ , N. ( 1970 ). On finite groups with given conjugate types II . Osaka J. Math. 7 : 231 – 251 .
   Google Scholar
• It⊚ , N. ( 1970 ). On finite groups with given conjugate types III . Math. Z. 117 : 267 – 271 .
   Google Scholar
• Rebmann , J. ( 1971 ). F-gruppen . Arch. Math. 22 : 225 – 230 .
   Google Scholar
• Communicated by A. Turull.
   Google Scholar