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Homogeneous monomial groups and centralizers
Date
2018-01-01
Author
Kuzucuoğlu, Mahmut
Sushchanskyy, Vitaly I.
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Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
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The construction of homogeneous monomial groups are given and their basic properties are studied. The structure of a centralizer of an element is completely described and the problem of conjugacy of two elements is resolved. Moreover, the classification of homogeneous monomial groups are determined by using the lattice of Steinitz numbers, namely, we prove the following: Let and be two Steinitz numbers. The homogeneous monomial groups sigma(H) and sigma(G) are isomorphic if and only if = and HG provided that the splittings of sigma(H) and sigma(G) are regular.
Subject Keywords
Centralizer of subgroup
,
Direct limit
,
Monomial group
URI
https://hdl.handle.net/11511/38696
Journal
COMMUNICATIONS IN ALGEBRA
DOI
https://doi.org/10.1080/00927872.2017.1324874
Collections
Department of Mathematics, Article
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M. Kuzucuoğlu and V. I. Sushchanskyy, “Homogeneous monomial groups and centralizers,”
COMMUNICATIONS IN ALGEBRA
, pp. 597–609, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/38696.