Russo, Francesco (2007) Generalized FC-groups in Finitary Groups. In: Group Theory Seminars in Michigan State University, 30 Ott 2007, East Lansing, USA. (Unpublished)

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Item Type: Conference or Workshop Item (Speech)
Title: Generalized FC-groups in Finitary Groups
Creators:
CreatorsEmail
Russo, Francescofrancesco.russo@dma.unina.it
Date: 30 October 2007
Date Type: Publication
Number of Pages: 31
Event Type: Workshop
Event Title: Group Theory Seminars in Michigan State University
Event Location: East Lansing, USA
Event Dates: 30 Ott 2007
Date: 30 October 2007
Number of Pages: 31
Uncontrolled Keywords: Conjugacy classes; linear PC-groups; linear CC-groups; PChypercentral series; CC-hypercentral series MSC 2000 : 20C07; 20D10; 20F24.
References: References [1] Ballester-Bolinches,A. and Ezquerro,L.M.: Classes of Finite Groups, Springer, Dordrecht, 2006. [2] Beidleman, J.C., Galoppo, A. and Manfredino, M. (1998). On PChypercentral and CC-hypercentral groups. Comm. Alg. 26, 3045-3055. [3] Doerk,K. and Hawkes,T.: Finite Soluble Groups, de Gruyter, Berlin, 1992. [4] Franciosi, S., de Giovanni, F. and Tomkinson, M. J.(1990). Groups with polycyclic-by-finite conjugacy classes. Boll.UMI 4B, 35-55. [5] Franciosi, S., de Giovanni, F. and Tomkinson, M. J.(1991). Groups with Chernikov conjugacy classes. J. Austral. Math. Soc A50, 1-14. [6] Gara˘s˘cuk, M. S.(1960). On theory of generalized nilpotent linear groups. Dokl. Akad. Nauk BSSR [in Russian] 4 276-277. [7] Huppert,B.: Endliche Gruppen I, Springer, Berlin, 1967. [8] Landolfi, T. (1995). On generalized central series of groups. Ricerche Mat. XLIV, 337-347. [9] Leinen, F. and Puglisi,O. (1993). Unipotent finitary linear groups, J. London Math. Soc. (2) 48. [10] Leinen, F. (1996). Irreducible Representations of Periodic Finitary Linear Groups, J. Algebra 180, 517-529. [11] Maier,R., Anogolgues of Dietzmann’s Lemma. In: Advances in Group Theory 2002, Ed. F.de Giovanni, M.Newell, (Aracne, Roma, 2003), pp.43-69. [12] Meierfrankenfeld, U., Phillips, R.E. and Puglisi, O. (1993). Locally solvable finitary linear groups. J. London Math. Soc. (2) 47, 31-40. [13] Meierfrankenfeld, U. (1995). Ascending subgroups of irreducible finitary linear groups. J. London Math. Soc. (2) 51, 75-92. [14] Merzlyakov,Yu.I. Linear groups. In: Itogi Nauki i Tkhniki, Algebra Topologiya, Geometriya, vol.16, 1978, pp.35-89. [15] Murach,M.M. (1976). Some generalized FC groups of matrices. Ukr. Math. Journal 28, 92-97. [16] Phillips, R.E.(1988). The structure of groups of finitary transofrmations. J. Algebra 119, 400-448. [17] Pinnock,C.J.E., Supersolubility and finitary groups. Ph.D. Thesis. University of London, Queen Mary and Westfield College, London, 2000. [18] Platonov,V.P.(1967). Linear groups with identical relations. Dokl.Akad.Nauk BSSR [in Russian] 11, 581-582. [19] Platonov,V.P.(1969). On a problem of Mal’cev. Math USSR Sb 8, 599-602. [20] Robinson,D.J.S.: Finiteness conditions and generalized soluble groups, Springer, Berlin, 1972. [21] Robinson,D.J. and Wilson,J. (1984). Soluble groups with many polycyclic quotients. Proc. London Math. Soc. 48, 193-229. [22] Suprunenko,D.A.: Groups of Matrices. [in Russian] Nauka, Moscow, 1972. [23] Tomkinson,M.J., FC groups. Boston: Research Notes in Mathematics, 96, Pitman, 1994. [24] Wehrfritz,B. A. F. Infinite linear groups. Springer, Berlin, 1973. [25] Wehrfritz,B. A. F. (1993). Locally soluble finitary skew linear groups. J.Algebra 160, 226-241.
MIUR S.S.D.: Area 01 - Scienze matematiche e informatiche > MAT/03 - Geometria
Area 01 - Scienze matematiche e informatiche > MAT/02 - Algebra
Date Deposited: 18 Mar 2008
Last Modified: 30 Apr 2014 19:25
URI: http://www.fedoa.unina.it/id/eprint/1305

Abstract

A group $G$ is called $FC$-group if it is a group in which each element has finitely many conjugates. This condition is equivalent to require that $G/C_G(x^G)$ is a finite group for each element $x$ of $G$, where the symbol $x^G$ denotes the normal closure of the subgroup $\langle x \rangle$ in $G$. A group $G$ is called $CC$-group if $G/C_G(x^G)$ is a Chernikov group for each element $x$ of $G$. A group $G$ is called $PC$-group if $G/C_G(x^G)$ is a polycyclic-by-finite group for each element $x$ of $G$. $FC$-groups are subclasses of the classes of $CC$-groups and $PC$-groups. Here we investigate finitary linear groups which have generalized series of $CC$-groups and $PC$-groups.

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