Iranian Journal of Mathematical Sciences and Informatics مجله علوم ریاضی و انفورماتیک IJMSI Basic Sciences http://ijmsi.ir 1 admin 1735-4463 2008-9473 8 10.52547/ijmsi 14 8888 13 en jalali 1400 7 1 gregorian 2021 10 1 16 2 online 1 fulltext
en The Number of Subgroups of a Given Type in Certain Finite Groups عمومى General پژوهشي Research paper The number of subgroups, normal subgroups and characteristic subgroups of a finite group \$G\$ are denoted by \$Sub(G)\$, \$NSub(G)\$ and \$CSub(G)\$, respectively. The main goal of this paper is to present a matrix model for computing these positive integers for dicyclic groups, semi-dihedral groups,&nbsp; and three sequences \$U_{6n}\$, \$V_{8n}\$ and \$H(n)\$ of groups that can be presented as follows:<br> begin{eqnarray*}<br> U_{6n} &=& langle a, b mid a^{2n} = b^{3} = e, bab = arangle,<br> V_{8n} &=& langle a, b mid a^{2n} = b^{4} = e, aba = b^{-1}, ab^{-1}a = brangle,<br> H(n)&=&langle a,b,c mid a^{2^{n-2}}=b^{2}=c^{2}=e, [x,y]=[y,z]=e, x^{z}=xy rangle.<br> end{eqnarray*}<br> For each group, a matrix model containing all information is given. Subgroup, Normal subgroup, Characteristic subgroup. 73 87 http://ijmsi.ir/browse.php?a_code=A-10-704-2&slc_lang=en&sid=1 H. B. Shelash ameen.hayder81@gmail.com `10031947532846008814` 10031947532846008814 No Kufa University, Iraq A. R. Ashrafi ashrafi@kashanu.ac.ir `10031947532846008815` 10031947532846008815 Yes University of Kashan, Iran