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This article is cited in 7 scientific papers (total in 8 papers)
Normal subgroups of free periodic groups
S. I. Adian
Abstract:
In this paper the concept of metaperiodic word of a given exponent is introduced, and transformations (reversals) of such words are considered. It is proved that in a free periodic group $B(m,n)$ of any odd exponent $n\geqslant665$ with $m\geqslant66$ generators an infinite independent system of complementary relations can be singled out. It follows that in $B(m,n)$ there exist infinite ascending and descending chains of normal subgroups and also a recursively defined factor group of $B(m,n)$ with an unsolvable identity problem.
Bibliography: 4 titles.
Received: 28.05.1981
Citation:
S. I. Adian, “Normal subgroups of free periodic groups”, Math. USSR-Izv., 19:2 (1982), 215–229
Linking options:
https://www.mathnet.ru/eng/im1592https://doi.org/10.1070/IM1982v019n02ABEH001414 https://www.mathnet.ru/eng/im/v45/i5/p931
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Abstract page: | 473 | Russian version PDF: | 105 | English version PDF: | 15 | References: | 47 | First page: | 3 |
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