Equation 677 Database

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Magma 8de3fbbd326e…

magma 8de3fbbd326e
Size
595
Isomorphism class hash
8de3fbbd326ed297c8d04ccd79049d5b2197b2acce8f8d94f33cb9a1d2d3f949
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 23:34:52
Display reorder
37,36,38,35,33,34,160,159,161,156,157,158,179,178,177,174,175,176,388,387,389,384,385,386,492,497,493,494,495,496,539,514,535,588,559,143,142,141,140,138,139,149,148,147,144,145,146,15,17,16,19,20,18,0,1,2,88,89,87,195,191,187,183,256,253,233,232,234,235,236,248,240,249,239,238,247,237,92,91,90,93,94,95,485,484,480,481,482,483,335,334,330,331,332,333,316,315,317,312,313,314,376,375,377,372,373,374,490,489,491,486,487,488,477,476,478,479,474,475,416,415,417,418,419,414,341,340,336,337,338,339,532,552,533,523,543,518,525,550,587,571,592,593,555,558,564,586,206,205,207,209,210,208,227,226,228,231,229,230,252,255,182,192,184,188,117,119,118,116,114,115,24,26,25,21,22,23,32,31,30,28,29,27,86,85,84,83,81,82,220,222,221,224,225,223,433,432,434,435,436,437,459,458,460,461,456,457,268,267,269,264,265,266,504,509,505,506,507,508,358,357,359,354,355,356,448,447,449,444,445,446,278,277,279,280,281,276,381,380,382,383,378,379,545,522,549,529,512,542,548,513,583,590,575,560,580,582,574,569,128,127,126,131,129,130,137,136,135,132,133,134,64,63,65,68,66,67,44,43,42,40,41,39,49,48,50,46,47,45,12,14,13,11,9,10,74,73,72,71,69,70,123,125,124,121,122,120,362,361,363,364,365,360,442,441,443,438,439,440,503,502,498,499,500,501,271,270,272,273,274,275,467,466,462,463,464,465,367,366,368,369,370,371,404,403,405,406,407,402,326,325,327,328,329,324,536,520,531,524,515,519,530,511,594,556,568,585,561,554,581,584,198,197,196,201,199,200,203,202,204,218,219,217,251,257,181,194,186,190,55,54,56,51,52,53,80,79,78,77,75,76,163,162,164,165,166,167,111,113,112,108,109,110,155,154,153,152,150,151,286,285,287,282,283,284,430,429,431,426,427,428,398,397,399,400,401,396,298,297,299,294,295,296,309,308,310,311,306,307,302,301,303,304,305,300,410,409,411,412,413,408,421,420,422,423,424,425,544,528,547,516,521,541,534,537,591,563,567,578,565,566,562,570,104,103,102,107,105,106,3,5,4,7,8,6,59,58,57,60,61,62,96,98,97,101,99,100,193,189,185,180,254,250,241,243,242,246,244,245,216,215,214,213,211,212,170,169,168,171,172,173,322,321,323,318,319,320,471,470,472,473,468,469,353,352,348,349,350,351,395,394,390,391,392,393,290,289,291,292,293,288,263,262,259,258,260,261,345,344,346,347,342,343,450,455,451,452,453,454,527,546,510,526,540,517,538,551,553,577,572,579,573,589,557,576 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#54e3a19f93137e404c924a9b37966faa8299b270c95916aef4ed0fa8730aa82d, M = the submagma generated by {6, 24} (35 elements) in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 85.

last edited by qawbecrdtey at 2026-10-08 23:34:54 · history