Equation 677 Database

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Magma 87780628fcd0…

magma 87780628fcd0
Size
707
Isomorphism class hash
87780628fcd031b22d0eced9331acf9c3842411ad5c4e74a84407829dfb49ff7
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 10:11:51
Display reorder
74,73,75,76,77,72,706,143,142,139,140,141,138,116,115,117,118,119,114,136,135,137,132,133,134,102,107,103,104,105,106,6,11,7,8,9,10,121,120,122,123,124,125,81,80,82,83,78,79,330,331,332,333,334,335,128,127,129,130,131,126,113,112,108,109,110,111,324,329,325,326,327,328,399,401,400,402,403,404,590,589,588,591,592,593,533,532,534,374,372,373,413,412,411,414,415,416,545,544,546,574,575,573,380,379,378,377,375,376,599,598,597,594,596,595,604,603,605,602,600,601,407,406,405,409,410,408,647,646,638,632,639,650,649,648,640,690,670,682,684,683,705,704,703,700,701,702,224,223,226,227,222,225,243,242,244,245,240,241,177,176,178,179,174,175,256,255,257,252,253,254,233,232,228,229,230,231,94,93,95,90,91,92,212,211,213,214,215,210,301,300,302,303,304,305,323,322,318,319,320,321,85,84,86,87,88,89,315,314,316,317,312,313,572,571,570,587,568,569,473,472,471,474,475,476,449,448,447,450,451,452,460,459,461,464,462,463,469,468,470,467,465,466,458,457,456,455,453,454,480,482,481,479,477,478,494,493,492,489,490,491,487,486,488,483,484,485,609,634,610,637,608,635,642,606,643,666,679,699,661,664,698,688,687,669,676,685,149,148,145,146,147,144,154,153,155,150,151,152,14,13,15,16,17,12,162,167,163,164,165,166,156,161,157,158,159,160,65,64,60,61,62,63,19,18,20,21,22,23,46,45,47,42,43,44,273,272,274,275,270,271,59,58,54,55,56,57,101,100,96,97,98,99,540,539,541,538,543,542,560,559,558,555,557,556,528,527,529,526,524,525,355,354,356,359,357,358,530,561,531,536,537,535,518,520,519,521,522,523,503,502,501,505,506,504,516,515,517,514,513,567,550,551,586,554,552,553,623,633,615,611,636,616,621,629,618,677,678,692,671,659,693,691,675,672,660,689,0,1,3,4,5,2,68,67,69,70,71,66,265,264,266,267,268,269,32,31,33,34,35,30,53,52,48,49,50,51,277,276,278,279,280,281,291,290,292,293,288,289,309,308,310,311,306,307,282,287,283,284,285,286,36,41,37,38,39,40,295,294,296,297,298,299,563,562,579,566,564,565,427,426,428,425,423,424,421,420,422,419,417,418,365,364,363,360,361,362,434,433,432,429,430,431,442,441,443,445,446,444,369,371,370,368,366,367,437,436,435,438,439,440,512,511,510,508,509,507,622,607,619,620,613,612,644,645,641,697,667,686,694,668,695,696,674,681,673,680,259,258,261,262,263,260,209,208,204,205,206,207,218,217,219,220,221,216,247,246,248,249,250,251,238,237,239,234,235,236,196,195,197,192,193,194,173,172,168,169,170,171,187,186,188,189,190,191,29,28,24,25,26,27,199,198,200,201,202,203,183,182,184,185,180,181,347,346,345,344,342,343,582,581,580,583,584,585,548,547,549,578,576,577,353,352,351,348,349,350,384,386,385,382,383,381,387,389,388,390,391,392,341,340,339,336,338,337,393,395,394,397,398,396,500,499,498,496,497,495,624,627,626,625,617,614,630,631,628,656,654,665,657,651,662,663,658,652,653,655 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#83fb73755ed07f789756511d0e776415c2bd28bb0aaa387c6c265081499d5ced, M = {24, 25, 26, 27, 28, 29, 138} 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 10:11:53 · history