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<p>We consider the results of the action of an endomorphism <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation> of an abelian separable primary group <i>T</i> on an element <i>a</i> of the torsion-complete group <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\overline{B}\)</EquationSource> <EquationSource Format="MATHML"><math> <mover> <mi>B</mi> <mo>¯</mo> </mover> </math></EquationSource> </InlineEquation>, where <i>B</i> is a basic subgroup of the group <i>T</i>. It is shown that the element <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\alpha a\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mi>a</mi> </mrow> </math></EquationSource> </InlineEquation>, which lies in the cyclic subgroup formed by the element <i>a</i> or <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>, acts on only finitely many summands of the element <i>a</i> when it is represented as the sum of the elements of group <i>B</i> in a <i>p</i>-adic topology.</p>

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ENDOMORPHISMS OF A SEPARABLE PRIMARY GROUP

  • 期刊论文

  • 发表日期：

    2025年6月21日

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  • Tariel Kemoklidze

摘要

We consider the results of the action of an endomorphism \(\alpha \) α of an abelian separable primary group T on an element a of the torsion-complete group \(\overline{B}\) B ¯ , where B is a basic subgroup of the group T. It is shown that the element \(\alpha a\) α a , which lies in the cyclic subgroup formed by the element a or \(\alpha \) α , acts on only finitely many summands of the element a when it is represented as the sum of the elements of group B in a p-adic topology.