Infinite Groups with an Anticentral Element

REFERENCES

• Camina , A. R. ( 1978 ). Some conditions which almost characterize Frobenius groups. Israel . J. Math. 31 : 153 – 160 .
   Google Scholar
• Carter , R. W. ( 1993 ). Finite Groups of Lie Type-Conjugacy Classes and Complex Characters . West Sussex , England : John Wiley & Sons .
   Google Scholar
• Chillag , D. , MacDonald , I. D. ( 1984 ). Generalized Frobenius groups . Israel J. Math. 47 : 112 – 122 .
   Web of Science ®Google Scholar
• Chillag , D. , Mann , A. , Scoppola , C. M. ( 1988 ). Generalized Frobenius groups II . Israel J. Math. 62 : 269 – 282 .
   Web of Science ®Google Scholar
• Dark , R. , Scoppola , C. M. ( 1996 ). On Camina groups of prime power order . J. Algebra 181 : 787 – 802 .
   Web of Science ®Google Scholar
• Hartley , B. ( 1992 ). A general Brauer-fowler theorem and centralizers in locally finite groups . Pacific J. Math. 152 ( 1 ): 10 – 117 .
   Google Scholar
• Herzog , M. , Longobardi , P. , Maj , M. ( 2011 ). On infinite camina groups . Comm. Algebra 39 : 4403 – 4419 .
   Web of Science ®Google Scholar
• Isaacs , I. M. ( 1989 ). Coprime group actions fixing all nonlinear irreducible characters . Canad. J. Math. 41 : 68 – 82 .
   Web of Science ®Google Scholar
• Kegel , O. H. ( 1960/1961 ). Die Nilpotenz der Hp-Gruppen . Math. Z. 75 : 373 – 376 .
   Google Scholar
• Kegel , O. H. , Wehrfritz , B. ( 1973 ). Locally Finite Groups . Amsterdam-London : North-Holland Publishing Company .
   Google Scholar
• Ladisch , F. , ( 2008 ). Groups with anticentral elements . Comm. Algebra 36 : 2883 – 2894 .
   Web of Science ®Google Scholar
• Lewis , M. , ( 2010 ). Classifying Camina groups, A Theorem of Dark and Scoppola. arXiv:0807.0167v4 [math.GR]
   Google Scholar
• MacDonald , I. D. ( 1981 ). Some p-groups of Frobenius and extra-special type . Israel J. Math. 40 : 350 – 364 .
   Web of Science ®Google Scholar
• MacDonald , I. D. ( 1986 ). More p-groups of Frobenius type . Israel J. Math. 56 : 335 – 344 .
   Web of Science ®Google Scholar
• Meierfrankenfeld , U. , Phillips , R. E. , Puglisi , O. ( 1993 ). Locally solvable finitary linear groups . J. London Math. Soc. (2) 47 : 31 – 40 .
   Google Scholar
• Ren , Y. ( 1999 ). Applications of the theory of Camina groups . Chi. Ann. Math. 20B : 39 – 50 .
   Web of Science ®Google Scholar
• Robinson , D. J. S. ( 1995 ). A Course in the Theory of Groups. , 2nd ed. New York : Springer, GTM 80 .
   Google Scholar
• Springer , T. A. , Steinberg , R. ( 1970 ). Conjugacy classes. In: Seminar on Algebraic Groups and Related Finite Groups. Lecture Notes in Math. Vol. 131. Berlin: Springer-Verlag .
   Google Scholar
• Zhurtov , A. Kh. ( 2000 ). On regular automorphisms of order 3 and frobenius pairs . Siberian Math. J. 41 ( 2 ): 268 – 275 .
   Web of Science ®Google Scholar
• Communicated by A. Turull.
   Google Scholar