A polynomial automorphism of a group G is an automorphism of the form <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$g\mapsto (v_{1}^{-1}g^{\epsilon _{1}}v_{1})(v_{2}^{-1}g^{\epsilon _{2}}v_{2})\cdots (v_{k}^{-1}g^{\epsilon _{k}}v_{k})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>g</mi> <mo>↦</mo> <mrow> <mo stretchy="false">(</mo> <msubsup> <mi>v</mi> <mrow> <mn>1</mn> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msup> <mi>g</mi> <msub> <mi>ϵ</mi> <mn>1</mn> </msub> </msup> <msub> <mi>v</mi> <mn>1</mn> </msub> <mo stretchy="false">)</mo> </mrow> <mrow> <mo stretchy="false">(</mo> <msubsup> <mi>v</mi> <mrow> <mn>2</mn> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msup> <mi>g</mi> <msub> <mi>ϵ</mi> <mn>2</mn> </msub> </msup> <msub> <mi>v</mi> <mn>2</mn> </msub> <mo stretchy="false">)</mo> </mrow> <mo>⋯</mo> <mrow> <mo stretchy="false">(</mo> <msubsup> <mi>v</mi> <mrow> <mi>k</mi> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msup> <mi>g</mi> <msub> <mi>ϵ</mi> <mi>k</mi> </msub> </msup> <msub> <mi>v</mi> <mi>k</mi> </msub> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. In this paper, the structure of the group of polynomial automorphisms of a generalized extraspecial p-group is determined.

Polynomial automorphisms of a generalized extraspecial ${\varvec{p}}$-group

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2026年4月6日

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Tao Xu

摘要

A polynomial automorphism of a group G is an automorphism of the form $g\mapsto (v_{1}^{-1}g^{\epsilon _{1}}v_{1})(v_{2}^{-1}g^{\epsilon _{2}}v_{2})\cdots (v_{k}^{-1}g^{\epsilon _{k}}v_{k})$ $g \mapsto (v_{1}^{- 1} g^{ϵ_{1}} v_{1}) (v_{2}^{- 1} g^{ϵ_{2}} v_{2}) \dots (v_{k}^{- 1} g^{ϵ_{k}} v_{k})$ . In this paper, the structure of the group of polynomial automorphisms of a generalized extraspecial p-group is determined.

Polynomial automorphisms of a generalized extraspecial \({\varvec{p}}\)-group

摘要