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The order classes of 2-generator $$p$$-groups. (English) Zbl 1435.20025
Summary: In order to classify a finite group using its elements orders, the order classes are defined. This partition determines the number of elements for each order. The aim of this paper is to find the order classes of 2-generator $$p$$-groups of class 2. The results obtained here are supported by Groups, Algorithm and Programming (GAP).
##### MSC:
 20D15 Finite nilpotent groups, $$p$$-groups 20D60 Arithmetic and combinatorial problems involving abstract finite groups 20-08 Computational methods for problems pertaining to group theory
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##### References:
 [1] Al-Hasanat, B. N.; Ahmad, A.; Sulaiman, H.; Ababneh, F., Order classes of symmetric groups, International Journal of Applied Mathematics, 26, 4, 501-510, (2013) · Zbl 1301.20002 [2] Al-Hasanat, B.; Ahmad, A.; Sulaiman, H., The order classes of dihedral groups, Proceeding of Mathematical Sciences National Conference (SKSM21) [3] Du, X.; Shi, W., Finite groups with conjugacy classes number one greater than its same order classes number, Communications in Algebra, 34, 4, 1345-1359, (2006) · Zbl 1099.20013 [4] Das, A. K., On finite groups having perfect order subsets, International Journal of Algebra, 3, 13, 629-637, (2009) · Zbl 1197.20018 [5] Jones, L.; Toppin, K., On three questions concerning groups with perfect order subsets, Involve, 4, 3, 251-261, (2011) · Zbl 1261.20026 [6] Bacon, M. R.; Kappe, L.-C., On capable p-groups of nilpotency class two, Illinois Journal of Mathematics, 47, 1-2, 49-62, (2003) · Zbl 1030.20009 [7] Ahmad, A.; Magidin, A.; Morse, R. F., Two generator p-groups of nilpotency class 2 and their conjugacy classes, Publicationes Mathematicae Debrecen, 81, 1-2, 145-166, (2012) · Zbl 1257.20021 [8] Magidin, A., Capable 2-generator 2-groups of class two, Communications in Algebra, 34, 6, 2183-2193, (2006) · Zbl 1108.20015
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