Equation 677 Database

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Magma 92cf7e81688a…

magma 92cf7e81688a
Size
707
Isomorphism class hash
92cf7e81688a03c21113696673875e1d24f7fa9fee05d2f97966beced388a481
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
2026-10-08 03:07:14
Display reorder
245,244,243,240,242,241,644,60,62,61,63,64,65,194,193,192,195,196,197,233,232,231,228,229,230,70,69,71,68,66,67,189,191,190,188,186,187,227,226,225,224,222,223,270,272,271,275,273,274,237,239,238,235,236,234,258,260,259,261,262,263,279,281,280,277,278,276,559,558,560,561,562,563,332,331,333,334,335,330,553,552,554,555,556,557,325,324,326,327,328,329,382,381,383,378,379,380,570,575,571,572,573,574,499,498,500,501,502,503,577,576,578,579,580,581,592,591,593,588,589,590,494,493,495,496,497,492,615,622,623,612,611,613,642,628,625,634,686,706,699,695,694,681,676,698,700,693,78,80,79,81,82,83,88,87,89,86,84,85,74,73,72,75,76,77,211,210,212,215,213,214,92,91,90,94,95,93,100,99,101,97,98,96,106,105,107,102,103,104,19,18,20,23,21,22,157,156,158,160,161,159,206,205,204,207,208,209,464,463,465,466,467,462,389,388,384,385,386,387,455,454,450,451,452,453,449,448,444,445,446,447,527,526,522,523,524,525,546,551,547,548,549,550,509,508,504,505,506,507,587,586,582,583,584,585,368,367,369,370,371,366,365,364,360,361,362,363,651,648,653,637,636,638,641,633,621,630,674,665,688,679,667,668,682,677,662,680,7,6,8,10,11,9,257,253,252,254,255,256,31,30,32,35,33,34,37,36,38,41,39,40,27,29,28,26,24,25,199,198,200,202,203,201,56,55,54,58,59,57,136,135,137,134,132,133,47,46,45,44,42,43,124,123,125,122,120,121,407,406,402,403,404,405,530,529,531,532,533,528,315,314,316,317,312,313,418,417,419,414,415,416,431,430,426,427,428,429,420,425,421,422,423,424,413,412,408,409,410,411,321,320,322,323,318,319,564,569,565,566,567,568,475,474,476,477,478,479,650,654,656,647,640,645,632,629,620,616,675,684,685,663,658,689,660,666,659,664,128,127,126,131,129,130,174,176,175,178,179,177,12,14,13,16,17,15,139,138,140,143,141,142,248,246,247,250,251,249,283,284,282,285,286,287,169,168,170,171,172,173,220,219,221,218,216,217,0,1,2,4,5,3,268,267,269,266,265,264,338,337,339,340,341,336,307,311,306,308,309,310,513,512,514,515,510,511,395,394,390,391,392,393,433,432,434,435,436,437,373,372,374,375,376,377,473,472,468,469,470,471,461,460,456,457,458,459,346,345,347,342,343,344,545,544,540,541,542,543,652,655,649,639,646,643,635,631,624,619,678,683,687,673,661,657,670,672,669,671,167,166,165,164,162,163,305,304,303,301,300,302,150,152,151,154,155,153,110,109,108,111,112,113,293,292,291,289,290,288,50,49,48,53,51,52,183,185,184,182,180,181,144,146,145,148,149,147,117,119,118,114,115,116,295,296,294,298,299,297,359,358,354,355,356,357,399,398,400,401,396,397,348,353,349,350,351,352,605,604,600,601,602,603,520,519,521,516,517,518,441,440,442,443,438,439,595,594,596,597,598,599,539,538,534,535,536,537,480,485,481,482,483,484,487,486,488,489,490,491,626,617,627,606,608,607,614,618,609,610,690,702,704,692,701,691,697,703,705,696 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#54e3a19f93137e404c924a9b37966faa8299b270c95916aef4ed0fa8730aa82d, M = {24, 25, 26, 27, 28, 29, 135} 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 2026-10-08 03:07:15 · history