Khukhro, Evgeny (2013) Counterexamples to a rank analog of the ShepherdLeedhamGreenMckay theorem on finite pgroups of maximal nilpotency class. Siberian Mathematical Journal, 54 (1). pp. 173183. ISSN 00374466
Full content URL: http://link.springer.com/article/10.1134%2FS003744...
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Abstract
By the ShepherdLeedhamGreenMcKay theorem on finite pgroups of maximal nilpotency class, if a finite pgroup of order pn has nilpotency class n1, then f has a subgroup of nilpotency class at most 2 with index bounded in terms of p. Some counterexamples to a rank analog of this theorem are constructed that give a negative solution to Problem 16. 103 in The Kourovka Notebook. Moreover, it is shown that there are no functions r(p) and l(p) such that any finite 2generator pgroup whose all factors of the lower central series, starting from the second, are cyclic would necessarily have a normal subgroup of derived length at most l(p) with quotient of rank at most r(p). The required examples of finite pgroups are constructed as quotients of torsionfree nilpotent groups which are abstract 2generator subgroups of torsionfree divisible nilpotent groups that are in the Mal'cev correspondence with "truncated" Witt algebras. © 2013 Pleiades Publishing, Ltd.
Additional Information:  • Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 54, No. 1, pp. 225–239, January–February, 2013. 

Keywords:  Finite pgroup, Nilpotency class, Derived length, Lower central series, Rank 
Subjects:  G Mathematical and Computer Sciences > G110 Pure Mathematics 
Divisions:  College of Science > School of Mathematics and Physics 
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ID Code:  15578 
Deposited On:  28 Oct 2014 11:03 
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