Equation 677 Database

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Magma 7b4fff445e69…

magma 7b4fff445e69
Size
707
Isomorphism class hash
7b4fff445e69c3c2191d9ee19c0e56aa020f588ba12613cedd02b8705a9dbbb0
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 18:55:22
Display reorder
464,463,462,466,467,465,631,152,151,153,154,155,150,52,53,48,49,50,51,184,183,185,180,181,182,187,186,188,189,190,191,179,178,174,175,176,177,172,171,173,168,169,170,47,46,42,43,44,45,40,39,41,36,37,38,273,272,274,275,270,271,148,147,149,144,145,146,302,300,303,304,305,301,468,470,469,471,472,473,512,511,510,514,515,513,438,440,439,443,441,442,380,379,378,383,381,382,425,424,423,420,421,422,415,414,416,417,418,419,431,430,429,426,427,428,364,363,365,360,361,362,492,494,493,495,496,497,608,609,607,606,611,610,637,645,647,698,667,675,697,676,699,696,687,702,705,706,203,202,198,199,200,201,156,157,158,159,160,161,230,229,231,232,233,228,238,237,239,234,235,236,31,30,32,33,34,35,56,55,57,58,59,54,294,295,296,297,298,299,292,291,293,289,288,290,65,64,60,61,62,63,116,115,117,118,119,114,108,113,109,110,111,112,436,435,437,433,434,432,461,460,459,457,458,456,474,476,475,479,477,478,506,505,504,509,507,508,490,489,491,488,486,487,343,342,344,345,346,347,348,350,349,352,353,351,590,588,589,592,593,591,565,566,564,567,568,569,630,633,632,634,649,648,642,635,640,682,681,690,680,660,672,673,674,683,691,700,20,19,21,22,23,18,85,86,87,88,89,84,136,135,137,132,133,134,90,95,91,92,93,94,130,129,131,126,127,128,138,143,139,140,141,142,247,251,246,248,249,250,241,243,245,244,240,242,224,223,225,226,227,222,81,80,82,83,78,79,28,27,29,24,25,26,547,548,546,549,550,551,534,535,536,537,538,539,368,367,366,370,371,369,580,579,581,576,578,577,604,603,605,602,601,600,450,452,451,455,453,454,372,374,373,376,377,375,530,529,528,532,533,531,583,584,582,585,586,587,612,646,617,644,618,638,636,641,643,692,677,688,694,657,668,678,658,693,684,701,1,5,0,2,3,4,219,220,221,216,217,218,278,277,279,280,281,276,316,315,317,312,313,314,73,72,74,75,76,77,307,306,308,309,310,311,269,268,265,264,266,267,66,71,67,68,69,70,122,121,123,124,125,120,258,259,260,261,262,263,102,107,103,104,105,106,541,542,540,543,544,545,559,558,560,561,562,563,575,574,573,570,572,571,357,359,358,354,355,356,338,337,336,339,340,341,397,396,398,399,400,401,520,519,521,518,516,517,499,498,500,501,502,503,597,599,598,595,594,596,628,616,629,615,614,613,639,651,650,704,665,679,703,659,666,685,664,686,689,695,166,165,167,162,163,164,194,195,196,197,192,193,215,214,210,211,212,213,205,204,206,207,208,209,326,328,327,324,325,329,254,253,255,256,257,252,98,97,99,100,101,96,319,323,318,320,321,322,7,6,8,9,10,11,285,284,286,287,283,282,14,13,15,16,17,12,395,394,393,392,390,391,389,388,387,385,386,384,404,403,402,406,407,405,444,446,445,447,448,449,557,556,555,553,552,554,413,412,411,409,410,408,525,527,526,523,524,522,481,480,482,483,484,485,331,332,330,333,334,335,625,619,624,620,622,623,621,627,626,670,656,662,669,653,654,655,652,663,661,671 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 = {84, 85, 86, 87, 88, 89, 132} 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 18:55:23 · history