The Syzygetic Pencil of Cubics With a New Geometrical Development of Its Hesse G
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25) of thirty-six with identity form 9 cyclic 6^3's, or in all 36 more cyclic (rg's making the total number 40 cyclic G^n. These 6^3's separate the conies into sets of three and permute them in the set. Further, the collineations of period six in each set of 36 appear by twos in 9 cyclic Gq9, . A cyclic (rg, different from a dihedral (rg, contains two collineations of period 6, two of period 3, one of period 2, and identity. There are thus from each set of 36 collineations above mentioned, toge...ther with the 9 of period two and identity each time, nine cyclic G^b or in all 36 cyclic Gq&. These separate the conies into sets of nine. Two of the collineations of a G^ send one of the nine conies into itself, two more send the same conic into each of the other two of its natural set of three, and the remaining two, which are of period six, send it into one of the remaining six conies of the set of nine.
Jordan says, loc. Cit. P. 18, that a group G belonging to this (Hessian) type (of order 24*94)) contains a group H of order 27.
What to read after The Syzygetic Pencil of Cubics With a New Geometrical Development of Its Hesse G?
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To quickly assess the difficulty of the text, read a short excerpt:
25) of thirty-six with identity form 9 cyclic 6^3's, or in all 36 more cyclic (rg's making the total number 40 cyclic G^n. These 6^3's separate the conies into sets of three and permute them in the set. Further, the collineations of period six in each set of 36 appear by twos in 9 cyclic Gq9, . A cyclic (rg, different from a dihedral (rg, contains two collineations of period 6, two of period 3, one of period 2, and identity. There are thus from each set of 36 collineations above mentioned, toge...ther with the 9 of period two and identity each time, nine cyclic G^b or in all 36 cyclic Gq&. These separate the conies into sets of nine. Two of the collineations of a G^ send one of the nine conies into itself, two more send the same conic into each of the other two of its natural set of three, and the remaining two, which are of period six, send it into one of the remaining six conies of the set of nine.
Jordan says, loc. Cit. P. 18, that a group G belonging to this (Hessian) type (of order 24*94)) contains a group H of order 27.
What to read after The Syzygetic Pencil of Cubics With a New Geometrical Development of Its Hesse G?
You can find similar books in the "Read Also" column, or choose other free books by Charles Clayton Grove to read onlineMoreLess
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