We pursue further our investigation, begun in [H. Smith, Groups with all subgroups subnormal or nilpotent-by-Chernikov, Rend. Sem. Mat. Univ.Padova, 126 (2011), 245-253] and continued in [G. Cutolo and H. Smith, Locally finite groups with all subgroups subnormal or nilpotent-by-Chernikov. Centr. Eur. J. Math., (to appear)] of groups $G$ in which all subgroups are either subnormal or nilpotent-by-Chernikov. Denoting by $\mathfrak{X}$ the class of all such groups, our concern here is with locally finite p-groups in the class $\mathfrak{X}$, where $p$ is a prime, while an earlier article provided a reasonable classification of locally finite $\mathfrak{X}$ nb-groups in which all of the p-sections are nilpotent-by-Chernikov. Our main result is that if $G$ is a Baer p-group in $\mathfrak{X}$ then $G$ is nilpotent-by-Chernikov.
A.O. Asar (2000). Locally nilpotent p-groups whose proper subgroups are
hypercentral or nilpotent-by-Chernikov. J. London Math. Soc. (2). 61 (2), 412-422 C. Casolo (2002). On the structure of groups with all subgroups subnormal. J. Group Theory. 5 (3), 293-300 G. Cutolo and H. Smith Locally finite groups with all subgroups subnormal or nilpotent-by-Chernikov. Centr. Eur. J. Math.. E. Detomi (2003). Groups with many subnormal subgroups. J. Algebra. 264 (2), 385-396 M.R. Dixon, M.J. Evans and H. Smith (2000). Groups with all proper subgroups nilpotent-by-finite rank. Arch. Math. (Basel). 75 (2), 81-91 P. Hall (1958). Some sufficient conditions for a group to be nilpotent. Illinois J. Math.. 2, 787-801 W. Mohres (1989). Torsionsgruppen, deren Untergruppen alle subnormal sind. Geom. Dedicata. 31 (2), 237-244 W. Mohres (1990). Auflosbarkeit von Gruppen, deren Untergruppen alle
subnormal sind. Arch. Math. (Basel). 54 (3), 232-235 F. Napolitani and E. Pegoraro (1997). On groups with nilpotent by Chernikov proper subgroups. Arch. Math. (Basel). 69 (2), 89-94 H. Smith (1983). Hypercentral groups with all subgroups subnormal. Bull. London Math. Soc.. 15 (3), 229-234 H. Smith (2001). Groups with all non-nilpotent subgroups subnormal. Topics in infinite groups, Quad. Mat. Dept. Math., Seconda Univ. Napoli, Caserta. 8, 309-326 H. Smith (2001). On non-nilpotent groups with all subgroups subnormal. Ricerche Mat.. 50 (2), 217-221 H. Smith (2011). Groups with all subgroups subnormal or
nilpotent-by-Chernikov. Rend. Sem. Mat. Univ. Padova. 126, 245-253 H. Smith (2011). Groups that involve finitely many primes and have all subgroups subnormal. J. Algebra. 347 (1), 133-142
Cutolo, G., & Smith, H. (2012). Locally finite p-groups with all subgroups either subnormal or nilpotent-by-Chernikov. International Journal of Group Theory, 1(1), 39-45. doi: 10.22108/ijgt.2012.471
MLA
G. Cutolo; H. Smith. "Locally finite p-groups with all subgroups either subnormal or nilpotent-by-Chernikov". International Journal of Group Theory, 1, 1, 2012, 39-45. doi: 10.22108/ijgt.2012.471
HARVARD
Cutolo, G., Smith, H. (2012). 'Locally finite p-groups with all subgroups either subnormal or nilpotent-by-Chernikov', International Journal of Group Theory, 1(1), pp. 39-45. doi: 10.22108/ijgt.2012.471
VANCOUVER
Cutolo, G., Smith, H. Locally finite p-groups with all subgroups either subnormal or nilpotent-by-Chernikov. International Journal of Group Theory, 2012; 1(1): 39-45. doi: 10.22108/ijgt.2012.471