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Homogeneous monomial groups and centralizers

2018-01-01
Kuzucuoğlu, Mahmut
Oliynyk, Bogdana
Sushchanskyy, Vitaly I.
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.