Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-05T12:33:26.555Z Has data issue: false hasContentIssue false
  • English
  • Français

CHARACTERIZING n-ISOCLINIC CLASSES OF CROSSED MODULES

Part of: Other generalizations of groups Special categories Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  08 October 2018

HAJAR RAVANBOD ,
ALI REZA SALEMKAR  and
SAJEDEH TALEBTASH
HAJAR RAVANBOD*
Affiliation:
Faculty of Mathematical Sciences, Shahid Beheshti University, 1983963113, G.C., Tehran, Iran e-mails: [email protected], [email protected], [email protected]
ALI REZA SALEMKAR*
Affiliation:
Faculty of Mathematical Sciences, Shahid Beheshti University, 1983963113, G.C., Tehran, Iran e-mails: [email protected], [email protected], [email protected]
SAJEDEH TALEBTASH
Affiliation:
Faculty of Mathematical Sciences, Shahid Beheshti University, 1983963113, G.C., Tehran, Iran e-mails: [email protected], [email protected], [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, we introduce the notion of the equivalence relation, called n-isoclinism, between crossed modules of groups, and give some basic properties of this notion. In particular, we obtain some criteria under which crossed modules are n-isoclinic. Also, we present the notion of n-stem crossed module and, under some conditions, determine them within an n-isoclinism class.

MSC classification

Primary: 18B99: None of the above, but in this section
Secondary: 20E34: General structure theorems 20N99: None of the above, but in this section
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 61 , Issue 3 , September 2019 , pp. 637 - 656
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

References

REFERENCES

Arias, D. and Ladra, M., The precise center of a crossed module, J. Group Theory 12 (2009), 247–269.CrossRefGoogle Scholar
Beyl, F. R. and Tappe, J., Group extensions, representations, and the Schur multiplicator, Lecture Notes in Mathematics, 958 (Springer-Verlag, Berlin, 1982).CrossRefGoogle Scholar
Bioch, J. C., n-Isoclinism groups, Indag. Math. 38 (1976), 400–407.Google Scholar
Bioch, J. C. and van der Waall, R. W., Monomiality and isoclinism of groups, J. R. Angew. Math. 298 (1978), 74–88.Google Scholar
Blackburn, S. R., Enumeration within isoclinism classes of groups of prime power order, J. Lond. Math. Soc. 50 (2) (1994), 293–304.CrossRefGoogle Scholar
Burns, J. and Ellis, G., On the nilpotent multipliers of a group, Math. Z. 226 (1997), 405–428.CrossRefGoogle Scholar
Carrasco, P., Cegarra, A. M. and Grandjean, A. R., (Co)Homology of crossed modules, J. Pure Appl. Algebra 168 (2002), 147–176.CrossRefGoogle Scholar
Grandjean, A. R. and Ladra, M., On totally free crossed modules, Glasgow Math. J. 40 (1998), 323–332.CrossRefGoogle Scholar
Grandjean, A. R. and Ladra, M., H 2(T, G, σ) and central extensions for crossed modules, Proc. Edinburgh Math. Soc. 42 (1999), 169–177.CrossRefGoogle Scholar
Hall, M. and Senior, J. K., The groups of order 2n (n ≤ 6) (Macmillan Co., New York, 1964).Google Scholar
Hall, P., The classification of prime-power groups, J. R. Angew. Math. 182 (1940), 130–141.Google Scholar
Hall, P., Verbal and marginal subgroups, J. R. Angew. Math. 182 (1940), 130–141.Google Scholar
Hanaki, A., Generalized isoclinism and characters of finite groups, Indag. Math. N.S. 6 (1995) 411–418.CrossRefGoogle Scholar
Hekster, N. S., On the structure of n-isoclinism classes of groups, J. Pure Appl. Algebra 40 (1986), 63–85.CrossRefGoogle Scholar
Hekster, N. S. and van der Waall, R. W., Monomiality and 2-isoclinism of groups, Indag. Math. 50 (1988), 263–276.CrossRefGoogle Scholar
Huppert, B. and Blackburn, N., Finite groups II (Springer, Berlin, 1982).CrossRefGoogle Scholar
Ishikawa, K., Finite p-groups up to isoclinism, which have only two conjugacy lengths, J. Algebra 220 (1999), 333–345.CrossRefGoogle Scholar
Ladra, M. and Grandjean, A. R., Crossed modules and homology, J. Pure Appl. Algebra 95 (1994), 41–55.CrossRefGoogle Scholar
Lescot, P., Isoclinism classes and commutativity degrees of finite groups, J. Algebra 177 (1995), 847–869.CrossRefGoogle Scholar
Loday, J.-L., Spaces with finitely many non-trivial homotopy groups, J. Pure Appl. Algebra 50 (1988), 179–202.Google Scholar
MacDonald, I. D., On central series, Proc. Edinburgh Math. Soc. 13 (1962), 175–178.CrossRefGoogle Scholar
Moghaddam, M. R. R., Salemkar, A. R. and Chiti, K., n-Isoclinism classes and n-nilpotency degree of finite groups, Algebra Colloq. 12 (2005), 225–261.CrossRefGoogle Scholar
Mohammadzadeh, H., Shahrokhi, S. and Salemkar, A. R., Some results on stem covers of crossed modules, J. Pure Appl. Algebra 218 (2014), 1964–1972.CrossRefGoogle Scholar
Norrie, K. J., Crossed modules and analogues of group theorems, Ph.D Thesis (King's College, University of London, London, 1987).Google Scholar
Odabaş, A., Uslu, E. Ö. and Ilgaz, E., Isoclinism of crossed modules, J. Symb. Comput. 74 (2016), 408–424.CrossRefGoogle Scholar
Salemkar, A. R., Mohammadzadeh, H. and Shahrokhi, S., Isoclinism of crossed modules, Asian-Eur. J. Math. 9 (2016), 1650091–1–165009–12.CrossRefGoogle Scholar
Salemkar, A. R., Talebtash, S. and Riyahi, Z., The nilpotent multipliers of crossed modules, J. Pure Appl. Algebra 221 (2017), 2119–2131.CrossRefGoogle Scholar
Vieites, A. M. and Casas, J. M., Some results on central extensions of crossed modules, Homology Homotopy Appl. 4 (2002), 29–42.Google Scholar
van der Waall, R. W., On n-isoclinic embedding of n-isoclinic groups, Indag. Mathem. N.S. 15 (2004), 595–600.CrossRefGoogle Scholar
van der Waall, R. W., On n-isoclinic embedding of groups, J. Pure Appl. Algebra 52 (1988), 165–171.CrossRefGoogle Scholar