ON FREE SUBGROUPS OF FINITE EXPONENT IN CIRCLE GROUPS OF FREE NILPOTENT ALGEBRAS

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HANSMANN JULIANE

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Journal Paper

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Journal: INTERNATIONAL JOURNAL OF GROUP THEORY Year:2019 | Volume:8 | Issue:2 Page(s): 29-40

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Title

ON FREE SUBGROUPS OF FINITE EXPONENT IN CIRCLE GROUPS OF FREE NILPOTENT ALGEBRAS

Author(s)

HANSMANN JULIANE | Issue Writer Certificate

Keywords

groups of finite exponent

relatively free groups

circle group

free nilpotent algebra

algebra group

Abstract

Let K be a commutative ring with identity and N the free nilpotent K-algebra on a nonempty 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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APA: Copy

HANSMANN, JULIANE. (2019). ON FREE SUBGROUPS OF FINITE EXPONENT IN CIRCLE GROUPS OF FREE NILPOTENT ALGEBRAS. INTERNATIONAL JOURNAL OF GROUP THEORY, 8(2), 29-40. SID. https://sid.ir/paper/725204/en

Vancouver: Copy

HANSMANN JULIANE. ON FREE SUBGROUPS OF FINITE EXPONENT IN CIRCLE GROUPS OF FREE NILPOTENT ALGEBRAS. INTERNATIONAL JOURNAL OF GROUP THEORY[Internet]. 2019;8(2):29-40. Available from: https://sid.ir/paper/725204/en

IEEE: Copy

JULIANE HANSMANN, “ON FREE SUBGROUPS OF FINITE EXPONENT IN CIRCLE GROUPS OF FREE NILPOTENT ALGEBRAS,” INTERNATIONAL JOURNAL OF GROUP THEORY, vol. 8, no. 2, pp. 29–40, 2019, [Online]. Available: https://sid.ir/paper/725204/en

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