Orfi, R. (2014). Maximal subsets of pairwise non-commuting elements of $p$-groups of order less than $p^6$. International Journal of Group Theory, 3(1), 65-72.
Reza Orfi. "Maximal subsets of pairwise non-commuting elements of $p$-groups of order less than $p^6$". International Journal of Group Theory, 3, 1, 2014, 65-72.
Orfi, R. (2014). 'Maximal subsets of pairwise non-commuting elements of $p$-groups of order less than $p^6$', International Journal of Group Theory, 3(1), pp. 65-72.
Orfi, R. Maximal subsets of pairwise non-commuting elements of $p$-groups of order less than $p^6$. International Journal of Group Theory, 2014; 3(1): 65-72.
Maximal subsets of pairwise non-commuting elements of $p$-groups of order less than $p^6$
Let $G$ be a non-abelian group of order $p^n$, where $n\leq 5$ in which $G$ is not extra special of order $p^5$. In this paper we determine the maximal size of subsets $X$ of $G$ with the property that $xy\neq yx$ for any $x,y$ in $X$ with $x\neq y$.
A. Abdollahi, S. Akbari and H. R. Maimani (2006). Non-commuting graph of a group. J. Algbera. 298 (2), 468-492
2
A. Azad and Cheryl E. Praeger (2009). Maximal subsets of pairwise non-commuting elements of three-dimensional general linear
groups. Bull. Aus. Math. Soc.. 80 (1), 91-104
3
A. Azad, S. Fouladi and R. Orfi (2013). Maximal subsets of pairwise non-commuting elements of some finite $p$-groups. Bull. Iranian Math. Soc.. 39 (1), 187-192
4
Y. Berkovich (2008). Groups of prime power order. Walter de Gruyter, Berlin. 1
5
A. Y. M. Chin (2005). On non-commuting sets in an extraspecial $p$-group. J. Group Theory. 8 (2), 189-194
6
S. Fouladi and R. Orfi (2011). Maximal subsets of pairwise non-commuting elements of some $p$-groups of maximal class. Bull. Aust. Math. Soc.. 84 (3), 447-451
7
S. Fouladi and R. Orfi (2013). Maximum size of subsets of pairwise
non-commuting elements in finite metacyclic $p$-groups. Bull. Aust. Math. Soc.. 87 (1), 18-23
8
The GAP Group (2008). GAP - - Groups, Algorithms, and Programming. Version 4.4.12, http://www.gap-system.org.
9
C. R. Leedham-Green and S. McKay (2002). The Structure of Groups of Prime Power Order. of
London Mathematical Society Monographs, Oxford
University Press, Oxford. 27
10
R. James (1980). The Groups of Order p^6 p an
odd prime. Math. Comp.. 34 (150), 613-637
11
B. H. Neumann (1976). A problem of Paul Erd$ddot o$s on groups. J. Austral. Math. Soc. Ser. A. 21 (4), 467-472
12
L. Pyber (1987). The number of pairwise non-commuting
elements and the index of the centre in a finite group. J.
London Math. Soc. (2). 35, 287-295
13
D. M. Rocke (1975). p-groups with abelian centralizers. Proc. London Math. Soc. (3). 30, 55-75
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