Equation 677 Database

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Magma 5024a6647397…

magma 5024a6647397
Size
707
Isomorphism class hash
5024a6647397a70e1d52cab39c774edb1e591acbcb5cf2eeadec574b3230dc19
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
2026-10-06 18:48:09
Display reorder
46,45,47,42,43,44,706,286,285,287,282,283,284,161,156,157,158,159,160,217,216,218,219,220,221,109,108,110,111,112,113,192,197,193,194,195,196,293,292,288,289,290,291,222,227,223,224,225,226,177,176,178,179,174,175,300,301,302,303,304,305,298,299,294,296,297,295,501,503,502,504,505,506,392,528,391,389,390,388,553,552,554,555,556,557,546,545,544,548,549,547,497,496,498,529,500,499,468,467,466,469,470,471,323,325,324,328,326,327,331,330,329,332,333,334,401,400,399,403,404,402,412,411,413,415,416,414,613,609,608,606,633,614,644,635,641,607,699,675,696,703,700,691,695,704,705,702,242,241,243,244,245,240,251,246,247,248,249,250,125,124,120,121,122,123,254,253,255,256,257,252,204,209,205,206,207,208,37,36,38,39,40,41,133,132,134,135,136,137,228,233,229,230,231,232,239,238,234,235,236,237,130,129,131,126,127,128,521,523,522,524,525,526,542,541,543,550,539,540,384,383,382,386,387,385,346,345,344,342,343,341,428,430,429,425,426,427,368,367,369,366,364,365,433,432,431,435,436,434,423,422,424,421,419,420,361,363,362,360,358,359,374,373,375,371,372,370,629,624,626,623,625,628,618,617,619,627,701,693,692,680,671,669,670,676,682,683,89,88,84,85,86,87,83,78,79,80,81,82,16,15,17,12,13,14,212,211,213,214,215,210,64,63,65,60,61,62,56,55,57,58,59,54,114,119,115,116,117,118,23,22,18,19,20,21,8,7,9,10,11,6,199,198,200,201,202,203,447,446,448,444,445,443,320,322,321,319,317,318,527,313,312,316,314,315,308,306,307,310,311,309,407,406,405,410,408,409,450,449,520,453,451,452,455,454,456,457,458,459,561,563,562,558,560,559,508,507,509,510,511,512,538,537,536,418,551,417,637,612,639,611,636,638,642,622,643,621,694,690,681,686,665,678,663,687,677,697,26,25,27,28,29,24,52,53,48,49,50,51,3,2,4,5,1,0,140,139,141,142,143,138,94,93,95,90,91,92,277,281,276,278,279,280,32,31,33,34,35,30,266,265,267,268,269,264,263,262,258,259,260,261,271,275,270,272,273,274,532,531,530,535,533,534,599,598,597,594,596,595,376,378,377,381,379,380,569,568,567,564,566,565,604,603,605,600,602,601,571,572,570,574,575,573,581,580,579,576,578,577,582,583,584,587,585,586,439,438,437,441,442,440,590,588,589,593,591,592,651,645,648,646,647,650,640,653,649,654,698,674,679,689,673,672,664,688,684,685,146,145,147,148,149,144,171,172,173,168,169,170,77,76,72,73,74,75,189,188,190,191,186,187,68,67,69,70,71,66,96,101,97,98,99,100,102,107,103,104,105,106,167,166,162,163,164,165,185,184,180,181,182,183,150,155,151,152,153,154,489,488,487,486,484,485,483,482,481,479,480,478,494,493,495,490,491,492,519,518,517,515,516,514,354,353,355,513,357,356,462,461,460,463,464,465,473,472,474,475,476,477,347,349,348,351,352,350,335,337,336,340,338,339,396,398,397,393,394,395,620,632,630,652,631,610,616,615,634,655,668,659,662,666,657,658,656,660,661,667 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#3577482bd341efd08404d9d1bdf0973fd33301f1401bf0112f6bd2c4e9ff916f, M = {48, 49, 50, 51, 52, 53, 141} 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 2026-10-06 18:48:10 · history