Equation 677 Database

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Magma c049d817c6c3…

magma c049d817c6c3
Size
707
Isomorphism class hash
c049d817c6c37a49acc0577275ba7f022561219f11ed694be336da8361f9b7ed
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 706) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 09:02:57
Display reorder
25,24,26,27,28,29,706,86,88,89,84,85,87,242,240,243,244,245,241,331,335,330,332,333,334,229,233,228,230,231,232,16,15,17,12,13,14,55,54,56,57,58,59,187,186,188,189,190,191,198,203,199,200,201,202,179,178,174,175,176,177,304,303,305,300,301,302,327,326,318,325,324,328,574,372,373,375,376,374,409,408,407,412,410,411,571,573,572,570,569,568,509,511,510,512,513,514,521,523,522,524,525,526,498,497,499,502,500,501,347,346,345,343,344,342,420,419,421,422,423,424,426,425,427,428,429,430,623,619,611,621,620,622,613,618,612,700,669,667,684,682,697,701,699,696,704,705,46,42,43,44,45,47,273,272,274,275,270,271,264,269,265,266,267,268,259,258,260,261,262,263,251,250,246,247,248,249,37,36,38,39,40,41,148,147,149,144,145,146,116,115,117,118,119,114,111,110,112,113,108,109,10,9,11,6,7,8,102,107,103,104,105,106,403,402,401,406,404,405,448,447,446,445,443,444,459,458,460,455,456,457,561,560,562,557,559,558,449,451,450,452,453,454,467,469,468,471,472,470,486,485,487,488,489,490,432,431,433,434,436,435,483,482,484,479,480,481,633,614,629,631,630,632,615,610,616,691,670,678,657,662,671,674,688,665,687,702,171,173,168,169,170,172,155,154,150,151,152,153,181,180,182,183,184,185,98,97,99,100,101,96,239,238,235,234,236,237,158,157,159,160,161,156,20,19,21,22,23,18,49,48,50,51,52,53,216,221,217,218,219,220,253,252,254,255,256,257,291,290,292,293,288,289,567,566,575,564,565,563,546,547,545,548,549,550,544,543,542,539,541,540,390,389,391,393,394,392,384,383,385,387,388,386,400,399,398,395,396,397,555,554,556,552,551,553,495,494,496,491,492,493,594,595,596,597,598,599,628,606,627,609,608,626,625,641,639,695,681,677,668,658,676,690,680,683,686,698,283,285,286,287,282,284,329,323,319,320,321,322,211,210,212,213,214,215,138,143,139,140,141,142,279,278,280,281,276,277,135,134,136,137,132,133,34,33,35,30,31,32,295,299,294,296,297,298,226,225,227,223,222,224,167,166,162,163,164,165,1,5,0,2,3,4,381,380,382,378,379,377,437,439,438,440,441,442,590,588,589,592,593,591,581,580,579,578,577,576,587,586,585,584,583,582,352,351,353,350,348,349,476,478,477,475,473,474,466,465,464,462,463,461,535,534,533,537,538,536,624,636,607,617,647,648,637,634,635,703,666,664,693,661,685,692,679,675,689,694,309,311,307,306,308,310,122,121,123,124,125,120,61,60,62,63,64,65,66,71,67,68,69,70,75,74,76,77,72,73,128,127,129,130,131,126,313,317,312,314,315,316,82,81,83,78,79,80,92,91,93,94,95,90,204,209,205,206,207,208,193,192,194,195,196,197,600,601,602,604,605,603,528,527,529,531,532,530,417,416,418,413,414,415,520,519,518,517,515,516,508,507,506,505,503,504,358,357,359,356,354,355,340,339,341,337,336,338,366,368,367,371,369,370,363,365,364,362,360,361,638,642,640,644,645,646,643,649,650,673,653,655,652,651,656,659,663,654,660,672 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 707 = 7 + 5*140, 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#10604212f7d4a7b51fd21a22d9c743e5a67297285884dbf7fd2d260472af6645, M = {18, 19, 20, 21, 22, 23, 146} 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, 140): MacNeish's product over GF(4) x GF(5) x GF(7); GF(4) = F_2[x]/(x^2 + 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: 101.

last edited by qawbecrdtey at 2026-10-07 09:02:58 · history