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ON FREE SUBGROUPS OF FINITE EXPONENT IN CIRCLE GROUPS OF FREE NILPOTENT ALGEBRAS
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نویسنده
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hansmann juliane
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منبع
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international journal of group theory - 2019 - دوره : 8 - شماره : 2 - صفحه:29 -40
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چکیده
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Let k be a commutative ring with identity and n the free nilpotent k-algebra on a non-empty set x. then n is a group with respect to the circle composition. we prove that the subgroup generated by x is relatively free in a suitable class of groups, depending on the choice of k. moreover, we get unique representations of the elements in terms of basic commutators. in particular, if k is of characteristic 0 the subgroup generated by x is freely generated by x as a nilpotent group.
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کلیدواژه
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groups of nite exponent ,relatively free groups ,circle group ,free nilpotent algebra ,algebra group.
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آدرس
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university of kiel, department of mathematics, Germany
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پست الکترونیکی
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hansmann@math.uni-kiel.de
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Authors
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