Equation 677 Database

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Magma 577b86b23b06…

magma 577b86b23b06
Size
707
Isomorphism class hash
577b86b23b0646623eab5312327f3c473b8bb7bd85c9d969c4aef3223997a058
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 14:58:57
Display reorder
578,580,579,576,577,575,642,209,205,204,207,208,206,153,152,154,155,150,151,236,235,237,238,239,234,343,342,344,345,346,347,194,193,195,196,197,192,130,129,131,126,127,128,3,2,4,5,1,0,215,214,210,211,212,213,149,148,144,145,146,147,227,226,222,223,224,225,173,172,168,169,170,171,182,181,183,184,185,180,469,468,470,472,473,471,368,367,366,371,369,370,363,365,364,361,360,362,558,557,559,562,560,561,458,457,456,461,459,460,438,440,439,443,441,442,423,425,424,421,422,420,415,414,416,417,418,419,610,612,607,609,611,608,632,635,685,697,653,683,682,654,704,696,702,706,699,700,94,90,95,92,93,91,275,274,270,271,272,273,50,49,51,52,53,48,63,62,64,65,60,61,262,261,263,258,259,260,298,297,299,294,295,296,283,282,284,285,286,287,98,97,99,100,101,96,11,10,6,7,8,9,116,115,117,118,119,114,58,57,59,54,55,56,109,108,110,111,112,113,564,563,565,567,568,566,489,491,490,486,487,488,535,534,533,538,536,537,481,480,482,485,483,484,549,548,550,546,547,545,526,525,524,522,523,521,501,494,502,500,492,493,510,509,511,512,513,514,614,623,606,634,624,615,636,633,688,687,673,671,681,649,679,669,680,703,661,676,138,140,139,142,143,141,313,312,314,315,316,317,179,178,174,175,176,177,219,218,220,221,216,217,301,300,302,303,304,305,311,310,306,307,308,309,241,240,242,243,244,245,133,132,134,135,136,137,230,229,231,232,233,228,188,187,189,190,191,186,200,199,201,202,203,198,25,24,26,27,28,29,433,432,434,436,437,435,430,429,431,427,428,426,603,605,604,601,600,602,476,475,474,477,478,479,444,446,445,447,448,449,599,598,597,594,596,595,454,453,455,452,450,451,462,464,463,467,465,466,629,630,621,622,619,625,618,637,674,698,666,690,667,650,692,689,684,701,657,664,102,104,103,106,107,105,331,330,332,333,334,335,292,291,293,288,289,290,276,281,277,278,279,280,122,121,123,124,125,120,253,252,254,255,256,257,42,47,43,44,45,46,31,30,32,33,34,35,40,39,41,36,37,38,89,88,84,85,86,87,266,265,267,268,269,264,82,81,83,78,79,80,588,590,589,591,592,593,586,585,584,583,581,582,520,519,518,517,515,516,495,497,496,499,503,498,504,505,587,506,507,508,556,555,554,552,553,551,543,542,544,541,539,540,527,529,528,532,530,531,613,620,627,617,626,628,616,631,675,705,651,694,663,648,691,686,670,695,677,672,358,355,359,356,357,354,12,17,13,14,15,16,72,77,73,74,75,76,321,320,322,323,318,319,349,350,348,351,352,353,19,18,20,21,22,23,66,71,67,68,69,70,164,163,165,166,167,162,160,159,161,156,157,158,340,339,341,336,337,338,328,327,329,324,325,326,251,250,246,247,248,249,391,390,392,394,395,393,387,389,388,384,385,386,378,380,379,381,382,383,403,402,404,407,405,406,398,397,396,401,399,400,372,374,373,377,375,376,570,569,571,574,572,573,413,412,411,409,410,408,646,639,640,643,641,644,645,638,662,693,652,665,678,647,658,660,659,668,656,655 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#7c5787f3763007370795fcf378d2af7959e084037efbb89592fd99450acc2142, M = {120, 121, 122, 123, 124, 125, 133} 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 14:58:58 · history