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Wilkens, Bettina. (1391). CH-groups which are finite $p$-groups. , 1(4), 9-23. doi: 10.22108/ijgt.2012.1509
Bettina Wilkens. "CH-groups which are finite $p$-groups". , 1, 4, 1391, 9-23. doi: 10.22108/ijgt.2012.1509
Wilkens, Bettina. (1391). 'CH-groups which are finite $p$-groups', , 1(4), pp. 9-23. doi: 10.22108/ijgt.2012.1509
Wilkens, Bettina. CH-groups which are finite $p$-groups. , 1391; 1(4): 9-23. doi: 10.22108/ijgt.2012.1509

CH-groups which are finite $p$-groups

International Journal of Group Theory
مقاله 2، دوره 1، شماره 4، اسفند 2012، صفحه 9-23    اصل مقاله (496.29 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2012.1509
نویسنده
Bettina Wilkens*
Lecturer at University of Botswana
چکیده
In their paper "Finite groups whose noncentral commuting elements have centralizers of equal size"‎, ‎S‎. ‎Dolfi‎, ‎M‎. ‎Herzog and E‎. ‎Jabara classify the groups in question‎- ‎which they call $ CH$-groups‎- ‎up to finite $p$-groups‎. ‎Our goal is to investigate the finite $p$-groups in the class‎. ‎The chief result is that a finite $p$-group that is a $ CH$-group either has an abelian maximal subgroup or is of class at most $p+1$‎. ‎Detailed descriptions‎, ‎in some cases characterisations up to isoclinism‎, ‎are given‎.
کلیدواژه‌ها
Finite-$p$-groups؛ AC-groups؛ conjugate rank
مراجع
M. Aschbacher (2001) Finite Group Theory Cambridge University Press, Cambridge
S. Dolfi, M. Herzog and E. Jabara (2010) Finite groups whose noncentral commuting elements have centralizers of equal size Bull. Aust. Math. Soc. 82, 293-304
M. Hall (1959) The theory of groups Macmillan, New York
B. Huppert (1967) Endliche Gruppen I Springer, Heidelberg
I. M. Isaacs (2008) Subgroups generated by small classes in finite groups Proc. Amer. Math. Soc. 136, 2299-3301
A. Mann (1978) Conjugacy classes in finite groups Israel J. Math. 31, 78-84
A. Mann (2006) Elements of minimal breadth in finite $p$-groups and Lie algebras J. Aust. Math. Soc. 81, 209-214
G. Parmeggiani and B. Stellmacher (1999) $p$-groups of small breadth J. Algebra 213 (1), 52-68
L.Verardi (1987) Semiextraspecial groups of exponent $p$ Ann. Mat. Pura. Appl. (4) 148, 131-171
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