<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">kemsu</journal-id><journal-title-group><journal-title xml:lang="ru">СибСкрипт</journal-title><trans-title-group xml:lang="en"><trans-title>SibScript</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2949-2122</issn><issn pub-type="epub">2949-2092</issn><publisher><publisher-name>Kemerovo State University</publisher-name></publisher></journal-meta><article-meta><article-id custom-type="elpub" pub-id-type="custom">kemsu-1257</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>Математика</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>MATHEMATICS</subject></subj-group></article-categories><title-group><article-title>О ГРУППАХ АВТОМОРФИЗМОВ БЕСКОНЕЧНО-ПОРОЖДЕННЫХ СВОБОДНЫХ АБЕЛЕВЫХ ГРУПП</article-title><trans-title-group xml:lang="en"><trans-title>ON THE GROUPS OF THE INFINITELY GENERATED FREE ABELIAN GROUPS AUTOMORPHISMS</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Толстых</surname><given-names>В. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Tolstykh</surname><given-names>V. A.</given-names></name></name-alternatives><bio xml:lang="ru"/><bio xml:lang="en"/><email xlink:type="simple">vladimirtolstykh@arel.edu.tr</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru">Стамбульский университет Арел<country>Турция</country></aff><aff xml:lang="en">Istanbul Arel University<country>Turkey</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2015</year></pub-date><pub-date pub-type="epub"><day>23</day><month>03</month><year>2016</year></pub-date><volume>1</volume><issue>2-1</issue><fpage>46</fpage><lpage>47</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Толстых В.А., 2015</copyright-statement><copyright-year>2015</copyright-year><copyright-holder xml:lang="ru">Толстых В.А.</copyright-holder><copyright-holder xml:lang="en">Tolstykh V.A.</copyright-holder><license license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://www.sibscript.ru/jour/article/view/1257">https://www.sibscript.ru/jour/article/view/1257</self-uri><abstract><p>Пусть A – бесконечно-порожденная свободная абелева группа. Мы показываем, что все автоморфизмы группы Aut(A) являются внутренними.</p></abstract><trans-abstract xml:lang="en"><p>Let A be an infinitely generated free abelian group. The paper shows that all automorphisms of the group Aut(A) are inner.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>свободные абелевы группы</kwd><kwd>бесконечно-порожденные группы</kwd><kwd>группы автоморфизмов</kwd></kwd-group><kwd-group xml:lang="en"><kwd>free abelian groups</kwd><kwd>infinitely generated groups</kwd><kwd>automorphism groups</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Dyer J., Formanek E. The automorphism group of a free group is complete // J. London Math. Soc. 11 (1975). Р. 181 – 190.</mixed-citation><mixed-citation xml:lang="en">Dyer J., Formanek E. The automorphism group of a free group is complete // J. London Math. Soc. 11 (1975). Р. 181 – 190.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Dyer J., Formanek E. Automorphism sequences of free nilpotent group of class two // Math. Proc. Camb. Phil. Soc. 79 (1976). P. 271 – 279.</mixed-citation><mixed-citation xml:lang="en">Dyer J., Formanek E. Automorphism sequences of free nilpotent group of class two // Math. Proc. Camb. Phil. Soc. 79 (1976). P. 271 – 279.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Dyer J., Formanek E. Characteristic subgroups and complete automorphism groups // Amer. J. Math. 99 (1977). P. 713 – 753.</mixed-citation><mixed-citation xml:lang="en">Dyer J., Formanek E. Characteristic subgroups and complete automorphism groups // Amer. J. Math. 99 (1977). P. 713 – 753.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Hua L. K., Reiner I. Automorphisms of the unimodular group // Trans. Amer. Math. Soc. 71 (1951). Р. 331 – 348.</mixed-citation><mixed-citation xml:lang="en">Hua L. K., Reiner I. Automorphisms of the unimodular group // Trans. Amer. Math. Soc. 71 (1951). Р. 331 – 348.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">O’Meara O. A general isomorphism theory for linear groups // J. Algebra. 44 (1977). Р. 93 – 142.</mixed-citation><mixed-citation xml:lang="en">O’Meara O. A general isomorphism theory for linear groups // J. Algebra. 44 (1977). Р. 93 – 142.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Tolstykh V. The automorphism tower of a free group // J. London Math. Soc. 61 (2000). P. 423 – 440.</mixed-citation><mixed-citation xml:lang="en">Tolstykh V. The automorphism tower of a free group // J. London Math. Soc. 61 (2000). P. 423 – 440.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Tolstykh V. Infinitely generated free nilpotent groups: completeness of the automorphism groups // Math. Proc. Camb. Phil. Soc. 147 (2009). P. 541 – 566.</mixed-citation><mixed-citation xml:lang="en">Tolstykh V. Infinitely generated free nilpotent groups: completeness of the automorphism groups // Math. Proc. Camb. Phil. Soc. 147 (2009). P. 541 – 566.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Tolstykh V. On the Bergman property for the automorphism groups of relatively free groups // J. London Math. Soc. (2) 73 (2006). P. 669 – 680.</mixed-citation><mixed-citation xml:lang="en">Tolstykh V. On the Bergman property for the automorphism groups of relatively free groups // J. London Math. Soc. (2) 73 (2006). P. 669 – 680.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Tolstykh V. Small conjugacy classes in the automorphism groups of relatively free groups // J. Pure Appl. Algebra. 215 (2011). P. 2086 – 2098.</mixed-citation><mixed-citation xml:lang="en">Tolstykh V. Small conjugacy classes in the automorphism groups of relatively free groups // J. Pure Appl. Algebra. 215 (2011). P. 2086 – 2098.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
