Italian journal of pure and applied mathematics, Jan 12, 2008
ABSTRACT The aim of this paper is to consider an open problem which was posed by R. Brown, D. L. ... more ABSTRACT The aim of this paper is to consider an open problem which was posed by R. Brown, D. L. Johnson and E. F. Robertson [in J. Algebra 111, 177-202 (1987; Zbl 0626.20038)]. The problem is to determine the non-Abelian tensor square G⊗G for the group GL(n,q) and other linear groups. Later, T. Hannebauer [in Arch. Math. 55, No. 1, 30-34 (1990; Zbl 0763.20012)] computed tensor square of groups SL(2,q), PSL(2,q), GL(2,q) and PGL(2,q) for all q≥5 and q≠9. In this article we improve the results given by Hannebauer [loc. cit.] to all linear groups SL(n,q), PSL(n,q), GL(n,q) and PGL(n,q) except for some small values of (n,q).
In mathematics, the energy of a graph is the sum of the values of the eigenvalues of the adjacenc... more In mathematics, the energy of a graph is the sum of the values of the eigenvalues of the adjacency matrix of the graph. This quantity is studied in the context of spectral graph theory. In this paper the concepts of non-commuting graph of dihedral groups are presented and the general formula for the energy of this associated graph is found.
Italian journal of pure and applied mathematics, Jan 12, 2008
ABSTRACT The aim of this paper is to consider an open problem which was posed by R. Brown, D. L. ... more ABSTRACT The aim of this paper is to consider an open problem which was posed by R. Brown, D. L. Johnson and E. F. Robertson [in J. Algebra 111, 177-202 (1987; Zbl 0626.20038)]. The problem is to determine the non-Abelian tensor square G⊗G for the group GL(n,q) and other linear groups. Later, T. Hannebauer [in Arch. Math. 55, No. 1, 30-34 (1990; Zbl 0763.20012)] computed tensor square of groups SL(2,q), PSL(2,q), GL(2,q) and PGL(2,q) for all q≥5 and q≠9. In this article we improve the results given by Hannebauer [loc. cit.] to all linear groups SL(n,q), PSL(n,q), GL(n,q) and PGL(n,q) except for some small values of (n,q).
In mathematics, the energy of a graph is the sum of the values of the eigenvalues of the adjacenc... more In mathematics, the energy of a graph is the sum of the values of the eigenvalues of the adjacency matrix of the graph. This quantity is studied in the context of spectral graph theory. In this paper the concepts of non-commuting graph of dihedral groups are presented and the general formula for the energy of this associated graph is found.
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