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A note on the nonabelian tensor square
Published 2012“…This paper, we determine the nonabelian tensor square G?G for special orthogonal groups SO n(F q) and spin groups Spinn (F q), where F q is a field with q elements.…”
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On the nonabelian tensor square and capability of groups of order p2q
Published 2011“…In this paper, we compute the nonabelian tensor square of the group G. It is also shown that G is capable if and only if either Z(G) = 1 or p < q and Gab=Zp×Zp .…”
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The nonabelian tensor squares and homological functors of some 2-engel groups
Published 2012“…Originated in homotopy theory, the nonabelian tensor square is a special case of the nonabelian tensor product. …”
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The nanobelian tensor square (GXG) of symplectic groups and projective symplectic groups
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The computation of the nonabelian tensor product of cyclic groups of order p2
Published 2012“…Compatible actions play a very important role in determining the nonabelian tensor product. The nonabelian tensor product, G⊗H, was introduced by Brown and Loday in 1984. …”
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Computing the nonabelian tensor square of metacyclic p-groups of nilpotency class two
Published 2013“…In addition, structures of some other groups such as the nonabelian tensor square and various homological functors including Schur multiplier and exterior square can be computed using this programme. …”
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The homological functors of some Abelian groups of prime power order
Published 2014“…The nonabelian tensor square of a group G introduced by Brown and Loday in 1987 is a special case of the nonabelian tensor product. …”
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On the computations of some homological functors of 2-Engel groups of order at most 16
Published 2011“…The homological functors including J (G) , ∇ (G) , exterior square, the Schur multiplier, Δ (G) , the symmetric square and J (G) of a group were originated in homotopy theory. The nonabelian tensor square which is a special case of the nonabelian tensor product is vital in the computations of the homological functors of a group. …”
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Capability and homological functors of infinite two - generator groups of nilpotency class two
Published 2009“…Brown and Loday in 1984 and 1987 introduced the nonabelian tensor square of a group to be a special case of the nonabelian tensor product which has its origin in algebraic K-theory as well as in homotopy theory. …”
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A homological invariant of certain torsion free crystallographic groups
Published 2020“…Several homological invariants namely the nonabelian tensor square, the exterior square and the Schur multiplier of groups have been of research interests by group theorists over the years. …”
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Homological invariants of 2-generator nontorsion groups of class 2
Published 2007“…Using their classification and non-abelian tensor squares, we determine certain homological invariants in R, such as the exterior square, the symmetric square and the Schur multiplier.…”
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Abelianization of some finite metacyclic 2-groups
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Homological functors of infinite 2-generator groups of nilpotency class two of type 1 and type 2
Published 2007“…cation and non-abelian tensor squares given by N.H. Sarmin in 2002, we determine certain homological functors in R such as the exterior square, the symmetric square and the Schur multiplier. …”
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Homological functors of infinite non abelian 2-generator groups of nilpotency class two-the composition theorem
Published 2009“…Using their classification and nonabelian tensor squares, we determine the homological functors in R such as the exterior square, the symmetric square and the Schur multiplier. …”
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The exterior squares of some crystallographic groups
Published 2013“…The exterior square of a group is the factor group of the nonabelian tensor square with the central subgroup of the group…”
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Compatible pair of nontrivial actions for some cyclic groups of 2-power order
Published 2015“…Compatible actions play a very important verification before the nonabelian tensor product can be computed. This paper gives the some exact number of compatible pairs of actions for some cyclic groups of 2-power order. …”
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Some homological functors of infinite non-abelian 2-generators groups of nilpotency class 2
Published 2007“…Using their classification and nonabelian tensor squares, the homological functors in R such as the exterior square, the symmetric square and the Schur multiplier are determined in the Composition Theorem as follows: Theorem 3 (Composotion Theorem). …”
Conference or Workshop Item