n-complete crossed modules and wreath products of groups
In this paper we examine the $n$-completeness of a crossed module and we show that if $X=(W_1,W_2,\partial)$ is an $n$-complete crossed module, where $W_i=A_i wr B_i$ is the wreath product of groups $A_i$ and $B_i$, then $A_i$ is at most $n$-complete, for $i=1,2.$ Moreover, we show that when $X=(W...
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Tokat Gaziosmanpasa University
2021-04-01
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| Series: | Journal of New Results in Science |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/1691990 |
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| author | B. Davvaz M.a. Dehghani |
| author_facet | B. Davvaz M.a. Dehghani |
| author_sort | B. Davvaz |
| collection | DOAJ |
| description | In this paper we examine the $n$-completeness of a crossed module and we show that if $X=(W_1,W_2,\partial)$ is an $n$-complete crossed module, where $W_i=A_i wr B_i$ is the wreath product of groups $A_i$ and $B_i$, then $A_i$ is at most $n$-complete, for $i=1,2.$ Moreover, we show that when $X=(W_1,W_2,\partial)$ is an $n$-complete crossed module, where $A_i$ is nilpotent and $B_i$ is nilpotent of class $n$, for $i=1,2$, then if $A_i$ is an abelian group, then it is cyclic of order $p_i.$ Also, if $W_i=C_ pwr C_2$, where $p$ is prime with $p>3$, $i=1,2$, then $X=(W_1,W_2,\partial)$ is not an $n$-complete crossed module. |
| format | Article |
| id | doaj-art-ddb1260bd3a04b76adc3586377569643 |
| institution | Kabale University |
| issn | 1304-7981 |
| language | English |
| publishDate | 2021-04-01 |
| publisher | Tokat Gaziosmanpasa University |
| record_format | Article |
| series | Journal of New Results in Science |
| spelling | doaj-art-ddb1260bd3a04b76adc35863775696432025-08-20T03:44:19ZengTokat Gaziosmanpasa UniversityJournal of New Results in Science1304-79812021-04-011013845142n-complete crossed modules and wreath products of groupsB. Davvaz0https://orcid.org/0000-0003-1941-5372M.a. Dehghani1https://orcid.org/0000-0001-6327-6416Yazd UniversityYazd UniversityIn this paper we examine the $n$-completeness of a crossed module and we show that if $X=(W_1,W_2,\partial)$ is an $n$-complete crossed module, where $W_i=A_i wr B_i$ is the wreath product of groups $A_i$ and $B_i$, then $A_i$ is at most $n$-complete, for $i=1,2.$ Moreover, we show that when $X=(W_1,W_2,\partial)$ is an $n$-complete crossed module, where $A_i$ is nilpotent and $B_i$ is nilpotent of class $n$, for $i=1,2$, then if $A_i$ is an abelian group, then it is cyclic of order $p_i.$ Also, if $W_i=C_ pwr C_2$, where $p$ is prime with $p>3$, $i=1,2$, then $X=(W_1,W_2,\partial)$ is not an $n$-complete crossed module.https://dergipark.org.tr/en/download/article-file/1691990crossed modulewreath productscommutator |
| spellingShingle | B. Davvaz M.a. Dehghani n-complete crossed modules and wreath products of groups Journal of New Results in Science crossed module wreath products commutator |
| title | n-complete crossed modules and wreath products of groups |
| title_full | n-complete crossed modules and wreath products of groups |
| title_fullStr | n-complete crossed modules and wreath products of groups |
| title_full_unstemmed | n-complete crossed modules and wreath products of groups |
| title_short | n-complete crossed modules and wreath products of groups |
| title_sort | n complete crossed modules and wreath products of groups |
| topic | crossed module wreath products commutator |
| url | https://dergipark.org.tr/en/download/article-file/1691990 |
| work_keys_str_mv | AT bdavvaz ncompletecrossedmodulesandwreathproductsofgroups AT madehghani ncompletecrossedmodulesandwreathproductsofgroups |