10\}\oplus\{0, 3, 6, 9, 12\} e_1\leq e_2 \leq\cdots\leq e_n |\mathrm{Aut}(P)| = \left(\prod_{k=1}^n{p^{d_k} - p^{k-1}}\right)\left(\prod_{j= 1}^n{(p^{e_j})^{n-d_j}}\right) \left(\prod_{i=1}^n{(p^{e_i-1} )^{n-c_i+1}}\right) c_k=\mathrm{min}\{r|e_r=e_k^{\ ,}\} d_k=\mathrm{max}\{r|e_r = e_k^{\,}\} |\mathrm{Aut}(P)|=(p^n-1)\cdot s(p^n-p^{n-1}) \mathrm{Aut}(P)\cong\mathrm{GL }(n,\mathbb{F}_ 74 = 7 x 10^1 + 4 x 10^0. since 7 x 10^1 = 70 + 4 x 10^0= 4, 70+4 = 74. In octal numerals each place is a power with base 8 for example 112= 1 x 8^2 + 1 x 8^1 + 2 x 8^0 since 1 x 8^2 = 64 + 12 x 8^0 = 2, 112 in octal is equal to 64+8+2 = 74xy = aman = am + n = an + m = anam = yx. x 8^1 = 8 \mathbb{Z}_{15}\cong\{0, 5, 10\}\oplus\{0, 3, 6, 9, 12\} e_1\leq e_2 \leq\cdots\leq e_n |\mathrm{Aut}(P)| = \left(\prod_{k=1}^n{p^{d_k} - p^{k-1}}\right)\left(\prod_{j= 1}^n{(p^{e_j})^{n-d_j}}\right) \left(\prod_{i=1}^n{(p^{e_i-1} )^{n-c_i+1}}\right) c_k=\mathrm{min}\{r|e_r=e_k^{\ ,}\} d_k=\mathrm{max}\{r|e_r = e_k^{\,}\} |\m