A subgroup $X$ of a group $G$ is almost normal if the index $|G:N_G(X)|$ is finite, while $X$ is nearly normal if it has finite index in the normal closure $X^G$. This paper investigates the structure of groups in which every (infinite) subgroup is either almost normal or nearly normal.
M. De Falco (2001). Groups with many nearly normal subgroups. Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8). 4 (2), 531-540 M. De Falco, F. de Giovanni and C. Musella (2010). Groups with finitely many normalizers of non-polycyclic subgroups. Algebra Colloq.. 17, 203-210 F. De Mari and F. de Giovanni (2005). Groups with few normalizer subgroups. Irish Math. Soc. Bull.. 56, 103-113 F. De Mari and F. de Giovanni (2006). Groups with finitely many normalizers of non-abelian subgroups. Ric. Mat.. 55, 311-317 F. De Mari and F. de Giovanni (2006). Groups with finitely many normalizers of subnormal subgroups. J. Algebra. 304, 382-396 F. De Mari and F. de Giovanni (2007). Groups with finitely many normalizers of non-nilpotent subgroups. Math. Proc. R. Ir. Acad.. 107A, 143-152 I. I. Eremin (1959). Groups with finite classes of conjugate abelian subgroups. Mat. Sb.. 47, 45-54 S. Franciosi and F. de Giovanni (1995). Groups satisfying the minimal condition on certain non-normal subgroups. Proceedings of “Groups
- Korea 1994}, de Gruyter, Berlin. , 107-118 B. Hartley (1988). Fixed points of automorphisms of certain locally finite groups and Chevalley groups. J. London Math. Soc.. 37, 421-436 L. A. Kurdachenko, S. S. Levishchenko and N. N. Semko (1983). Groups with almost normal infinite subgroups. Soviet Math. (Iz. VUZ). 27, 73-81 A. Mann and D. Segal (1990). Uniform finiteness conditions in residually finite groups. Proc. London Math. Soc.. 61, 529-545 B. H. Neumann (1954). Groups covered by permutable subsets. J. London Math. Soc.. 29, 236-248 B. H. Neumann (1955). Groups with finite classes of conjugate subgroups. Math. Z.. 63, 76-96 Y. D. Polovickiu{i} (1980). Groups with finite classes of conjugate infinite abelian subgroups. Soviet Math. (Iz. VUZ). 24, 52-59 D. J. S. Robinson (1972). Finiteness conditions and generalized soluble groups. Springer, Berlin. V. P. v Sunkov (1970). On the minimality problem for locally finite groups. Algebra and Logic. 9, 137-151 M. J. Tomkinson (1981). On theorems of B. H. Neumann concerning $FC$-groups. Rocky Mountain J. Math.. 11, 47-58 M. J. Tomkinson (1984). $FC$-groups. Pitman, Boston. D. I. Zaicev (1974). On solvable subgroups of locally solvable groups. Soviet Math. Dokl. (SSSR). 15, 342-354
de Giovanni, F. and Rainone, C. (2012). Infinite groups with many generalized normal subgroups. International Journal of Group Theory, 1(3), 39-49. doi: 10.22108/ijgt.2012.1223
MLA
de Giovanni, F. , and Rainone, C. . "Infinite groups with many generalized normal subgroups", International Journal of Group Theory, 1, 3, 2012, 39-49. doi: 10.22108/ijgt.2012.1223
HARVARD
de Giovanni, F., Rainone, C. (2012). 'Infinite groups with many generalized normal subgroups', International Journal of Group Theory, 1(3), pp. 39-49. doi: 10.22108/ijgt.2012.1223
CHICAGO
F. de Giovanni and C. Rainone, "Infinite groups with many generalized normal subgroups," International Journal of Group Theory, 1 3 (2012): 39-49, doi: 10.22108/ijgt.2012.1223
VANCOUVER
de Giovanni, F., Rainone, C. Infinite groups with many generalized normal subgroups. International Journal of Group Theory, 2012; 1(3): 39-49. doi: 10.22108/ijgt.2012.1223
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