On the clones of nilpotent groups with a verbal subgroup of prime order. (English) Zbl 1374.08003
Summary: We show that if \(G\) is a finite nilpotent group with a verbal subgroup of prime order then the clone of \(G\) is not determined by the subgroups of \(G^2\).
MSC:
| 08A40 | Operations and polynomials in algebraic structures, primal algebras |
| 20D30 | Series and lattices of subgroups |
| 20E15 | Chains and lattices of subgroups, subnormal subgroups |
| 20D15 | Finite nilpotent groups, \(p\)-groups |
References:
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| [3] | K. A. Kearnes and Á. Szendrei, Clones of finite groups, Algebra Universalis, 54 (2005), 23-52. · Zbl 1114.20014 |
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| [6] | J. Shaw, Commutator relations and the clones of finite groups, Algebra Universalis, 72 (2014), 29-52. · Zbl 1309.08003 |
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