Geodesic
ON THE CAPABILITY OF FINITELY GENERATED NON-TORSION GROUPS OF NILPOTENCY CLASS 2
Glasgow mathematical journal, Tome 53 (2011) no. 2, pp. 411-417

Voir la notice de l'article provenant de la source Cambridge University Press

A group is called capable if it is a central factor group. In this paper, we establish a necessary condition for a finitely generated non-torsion group of nilpotency class 2 to be capable. Using the classification of two-generator non-torsion groups of nilpotency class 2, we determine which of them are capable and which are not and give a necessary and sufficient condition for a two-generator non-torsion group of class 2 to be capable in terms of the torsion-free rank of its factor commutator group.
DOI : 10.1017/S001708951100019X
Mots-clés : 20D15, 20J05 
KAPPE, LUISE-CHARLOTTE; ALI, NOR MUHAINIAH MOHD; SARMIN, NOR HANIZA. ON THE CAPABILITY OF FINITELY GENERATED NON-TORSION GROUPS OF NILPOTENCY CLASS 2. Glasgow mathematical journal, Tome 53 (2011) no. 2, pp. 411-417. doi: 10.1017/S001708951100019X
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[1] 1.Ahmad, A., Magidin, A. and Morse, R. F., A new classification of 2-generator p-groups of class 2 (submitted). Google Scholar

[2] 2.Bacon, M. and Kappe, L. C., The nonabelian tensor square of a 2-generator p-group of class 2, Arch. Math. 61 (1993), 508–516. Google Scholar | DOI

[3] 3.Bacon, M. and Kappe, L. C., On capable p-groups of nilpotency class two, Illinois J. Math. 47 (2003), 49–62. Google Scholar | DOI

[4] 4.Baer, R., Groups with preassigned central and central quotient groups, Trans. Am. Math. Soc. 44 (1938), 387–412. Google Scholar | DOI

[5] 5.Beuerle, J. and Kappe, L. C., Infinite metacyclic groups and their nonabelian tensor squares, Proc. Edinburgh Math. Soc. 43 (2000), 651–662. Google Scholar | DOI

[6] 6.Beyl, F. R., Felgner, U. and Schmid, P., On groups occurring as center factor groups, J. Algebra 61 (1979), 161–177. Google Scholar | DOI

[7] 7.Brown, R., Johnson, D. L. and Robertson, E. F., Some computations of nonabelian tensor products of groups, J. Algebra 111 (1987), 177–202. Google Scholar | DOI

[8] 8.Ellis, G., Tensor products and q-crossed modules, J. Lond. Math. Soc. 2 (1995), 243–258. Google Scholar | DOI

[9] 9.Ellis, G., On the capability of groups, Proc. Edinburgh Math. Soc. 41 (1998), 487–495. Google Scholar | DOI

[10] 10.Hall, P., The classification of prime-power groups, J. Reine Angew. Math. 182 (1940), 130–141. Google Scholar | DOI

[11] 11.Kappe, L. C., Sarmin, N. H. and Visscher, M. P., Two-generator two-groups of class two and their nonabelian tensor squares, Glasgow Math. J. 41 (1999), 417–430. Google Scholar | DOI

[12] 12.Magidin, A., Capability of nilpotent products of cyclic groups, J. Group Theory 84 (2005), 431–452. Google Scholar

[13] 13.Magidin, A., Capable two-generator 2-groups of class two, Comm. Algebra 34 (2006), 2183–2193. Google Scholar | DOI

[14] 14.Magidin, A. and Morse, R. F., Certain homological functors of 2-generator p-group of class 2, Contemp. Math. 511 (2010), 127–166. Google Scholar | DOI

[15] 15.Sarmin, N. H., Infinite two-generator groups of class two and their nonabelian tensor squares, IJMMS 32 (2002), 615–625. Google Scholar

[16] 16.Trebenko, D. Y., Nilpotent groups of class two with two generators, Curr. Anal. Appl. 228 (1989), 201–208. Google Scholar

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