The Small Index Property for Free Nilpotent Groups

REFERENCES

• Bryant , R. , Evans , D. ( 1997 ). The small index property for free groups and relatively free groups . J. London Math. Soc. 55 ( 2 ): 363 – 369 .
   Web of Science ®Google Scholar
• Bryant , R. , Macedonska , O. ( 1989 ). Automorphisms of relatively free nilpotent groups of infinite rank . J. Algebra 121 : 388 – 398 .
   Web of Science ®Google Scholar
• Bryant , R. , Roman'kov , V. ( 1998 ). The automorphism groups of relatively free algebras . J. Algebra 209 : 713 – 723 .
   Web of Science ®Google Scholar
• Dixon , J. , Neumann , P. M. , Thomas , S. ( 1986 ). Subgroups of small index in infinite symmetric groups . Bull. London Math. Soc. 18 : 580 – 586 .
   Web of Science ®Google Scholar
• Hodges , W. ( 1993 ). Model Theory . Cambridge : University Press .
   Google Scholar
• Kechris , A. ( 1995 ). Classical Descriptive Set Theory . New York : Springer-Verlag .
   Google Scholar
• Macpherson , H. D. ( 1992 ). Maximal subgroups of infinite-dimensional linear groups . J. Austral. Math. Soc. (Series A) 53 : 338 – 351 .
   Web of Science ®Google Scholar
• Macpherson , H. D. , Neumann , P. M. ( 1990 ). Subgroups of infinite symmetric groups . J. London Math. Soc. 42 ( 2 ): 64 – 84 .
   Google Scholar
• O'Meara , O. A general isomorphism theory for linear groups . J. Algebra 44 : 93 – 142 .
   Web of Science ®Google Scholar
• McKenzie , R. ( 1971 ). On elementary types of symmetric groups . Algebra Universalis 1 : 13 – 20 .
   Google Scholar
• Magnus , W. , Karrass A., Solitar , D. ( 1966 ). Combinatorial Group Theory . Wiley .
   Google Scholar
• Tolstykh , V. ( 2005 ). What does the automorphism group of a free abelian group A know about A? In: Logic and its Applications, Contemp. Math. Vol. 380 . Providence , RI : Amer. Math. Soc. , pp. 283 – 296 .
   Google Scholar
• Tolstykh , V. ( 2006 ). On the Bergman property for the automorphism groups of relatively free groups . J. London Math. Soc. 73 ( 2 ): 669 – 680 .
   Web of Science ®Google Scholar
• Tolstykh , V. ( 2011 ). Small conjugacy classes in the automorphism groups of relatively free groups . J. Pure Appl. Algebra 215 : 2086 – 2098 .
   Web of Science ®Google Scholar
• Communicated by D. Macpherson.
   Google Scholar