Russo, Francesco (2007) Generalized FCgroups 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 (Unpublished)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 FCgroups in Finitary Groups  
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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 PCgroups; linear CCgroups; PChypercentral series; CChypercentral series MSC 2000 : 20C07; 20D10; 20F24.  
References:  References [1] BallesterBolinches,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 CChypercentral groups. Comm. Alg. 26, 30453055. [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 polycyclicbyfinite conjugacy classes. Boll.UMI 4B, 3555. [5] Franciosi, S., de Giovanni, F. and Tomkinson, M. J.(1991). Groups with Chernikov conjugacy classes. J. Austral. Math. Soc A50, 114. [6] Gara˘s˘cuk, M. S.(1960). On theory of generalized nilpotent linear groups. Dokl. Akad. Nauk BSSR [in Russian] 4 276277. [7] Huppert,B.: Endliche Gruppen I, Springer, Berlin, 1967. [8] Landolfi, T. (1995). On generalized central series of groups. Ricerche Mat. XLIV, 337347. [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, 517529. [11] Maier,R., Anogolgues of Dietzmann’s Lemma. In: Advances in Group Theory 2002, Ed. F.de Giovanni, M.Newell, (Aracne, Roma, 2003), pp.4369. [12] Meierfrankenfeld, U., Phillips, R.E. and Puglisi, O. (1993). Locally solvable finitary linear groups. J. London Math. Soc. (2) 47, 3140. [13] Meierfrankenfeld, U. (1995). Ascending subgroups of irreducible finitary linear groups. J. London Math. Soc. (2) 51, 7592. [14] Merzlyakov,Yu.I. Linear groups. In: Itogi Nauki i Tkhniki, Algebra Topologiya, Geometriya, vol.16, 1978, pp.3589. [15] Murach,M.M. (1976). Some generalized FC groups of matrices. Ukr. Math. Journal 28, 9297. [16] Phillips, R.E.(1988). The structure of groups of finitary transofrmations. J. Algebra 119, 400448. [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, 581582. [19] Platonov,V.P.(1969). On a problem of Mal’cev. Math USSR Sb 8, 599602. [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, 193229. [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, 226241.  
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 polycyclicbyfinite 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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