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Mat. Zametki, 2014, Volume 95, Issue 5, Pages 651–655 (Mi mz10444)  

This article is cited in 4 scientific papers (total in 4 papers)

Splitting Automorphisms of Order $p^k$ of Free Burnside Groups are Inner

V. S. Atabekyan

Yerevan State University

Abstract: It is proved that, if the order of a splitting automorphism of odd period $n\ge 1003$ of a free Burnside group $B(m,n)$ is equal to a power of some prime, then the automorphism is inner. Thus, an affirmative answer is given to the question concerning the coincidence of the splitting automorphisms of the group $B(m,n)$ with the inner automorphisms for all automorphisms of order $p^k$ ($p$ is a prime). This question was posed in 1990 in “Kourovka Notebook” (see the 11th edition, Question 11.36.b).

Keywords: free Burnside group $B(m,n)$, splitting automorphism, inner automorphism.

DOI: https://doi.org/10.4213/mzm10444

Full text: PDF file (443 kB)
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English version:
Mathematical Notes, 2014, 95:5, 586–589

Bibliographic databases:

Document Type: Article
UDC: 512.544.43
Received: 05.04.2013

Citation: V. S. Atabekyan, “Splitting Automorphisms of Order $p^k$ of Free Burnside Groups are Inner”, Mat. Zametki, 95:5 (2014), 651–655; Math. Notes, 95:5 (2014), 586–589

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. S. Atabekyan, “Automorphism groups and endomorphism semigroups of groups $B(m,n)$”, Algebra and Logic, 54:1 (2015), 58–62  mathnet  crossref  crossref  mathscinet  isi
    2. A. L. Gevorgyan, Sh. A. Stepanyan, “On automorphisms of some periodic products of groups”, Uch. zapiski EGU, ser. Fizika i Matematika, 2015, no. 2, 7–10  mathnet
    3. V. S. Atabekyan, “The automorphisms of endomorphism semigroups of free Burnside groups”, Int. J. Algebr. Comput., 25:4 (2015), 669–674  crossref  mathscinet  zmath  isi  elib  scopus
    4. S. I. Adian, V. S. Atabekyan, “Periodic products of groups”, J. Contemp. Math. Anal.-Armen. Aca., 52:3 (2017), 111–117  crossref  mathscinet  zmath  isi  scopus
  • Математические заметки Mathematical Notes
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