A Cayley map <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\mathcal {M}= CM(G,X,q)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">M</mi> <mo>=</mo> <mi>C</mi> <mi>M</mi> <mo stretchy="false">(</mo> <mi>G</mi> <mo>,</mo> <mi>X</mi> <mo>,</mo> <mi>q</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> is t-balanced if <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$q(x)^{-1} = q^t(x^{-1})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>q</mi> <msup> <mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>=</mo> <msup> <mi>q</mi> <mi>t</mi> </msup> <mrow> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> for all <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$x \in X$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>x</mi> <mo>∈</mo> <mi>X</mi> </mrow> </math></EquationSource> </InlineEquation>. In this paper, we classify the regular t-balanced Cayley maps on <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\mathbb {Z}_2$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">Z</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>-extensions of a cyclic group.

A classification of regular t-balanced Cayley maps on $\mathbb {Z}_2$-extensions of a cyclic group

期刊论文
发表日期：

2026年2月20日

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Young Soo Kwon,
Jihye Park

摘要

A Cayley map $\mathcal {M}= CM(G,X,q)$ $M = C M (G, X, q)$ is t-balanced if $q(x)^{-1} = q^t(x^{-1})$ $q {(x)}^{- 1} = q^{t} (x^{- 1})$ for all $x \in X$ $x \in X$ . In this paper, we classify the regular t-balanced Cayley maps on $\mathbb {Z}_2$ $Z_{2}$ -extensions of a cyclic group.

A classification of regular t-balanced Cayley maps on \(\mathbb {Z}_2\)-extensions of a cyclic group

摘要