Equation 677 Database

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Magma e04c9caa3959…

magma e04c9caa3959
Size
707
Isomorphism class hash
e04c9caa39593cc0721a3ebf9439a6ee201bf35abd05bd97cbab641c2f1bd06b
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 20:23:32
Display reorder
274,273,275,270,271,272,706,196,197,192,193,194,195,21,20,22,23,18,19,248,247,249,250,251,246,266,265,267,268,269,264,261,260,262,263,258,259,97,96,98,99,100,101,303,302,304,305,301,300,189,188,190,191,186,187,294,299,295,296,297,298,108,113,109,110,111,112,393,395,394,396,397,398,359,358,357,355,356,354,374,373,372,371,369,370,324,326,325,329,327,328,446,445,444,441,442,443,343,342,344,346,347,345,559,558,560,562,563,561,422,421,420,418,419,417,413,412,411,416,414,415,434,433,432,431,429,430,615,613,611,634,608,609,618,614,612,633,697,693,681,698,705,700,696,701,704,699,7,8,9,10,11,6,47,46,42,43,44,45,26,25,27,28,29,24,49,48,50,51,52,53,39,38,40,41,36,37,292,293,289,290,291,282,146,145,147,148,149,144,13,12,14,15,16,17,252,257,253,254,255,256,139,138,140,141,142,143,498,497,499,495,496,494,571,573,572,576,574,575,542,541,540,545,543,544,529,531,530,584,532,533,552,554,553,556,557,555,583,528,527,526,524,525,473,475,474,470,471,472,578,577,579,580,581,582,564,566,565,567,568,569,521,523,522,518,519,520,625,626,616,631,629,632,624,628,630,627,692,703,676,675,694,678,668,669,684,673,184,185,180,181,182,183,199,198,200,201,202,203,222,227,223,224,225,226,155,154,150,151,152,153,205,204,206,207,208,209,286,285,287,288,283,284,31,30,32,33,34,35,237,236,238,239,234,235,210,215,211,212,213,214,56,55,57,58,59,54,387,389,388,390,391,392,386,385,384,382,383,381,488,490,489,491,492,493,407,406,405,409,410,408,339,341,340,337,338,336,503,505,504,500,501,502,506,508,507,509,510,511,586,585,587,588,589,590,378,380,379,375,376,377,512,514,513,515,516,517,636,606,635,617,639,640,607,610,622,623,690,702,672,682,688,689,667,674,671,686,134,135,136,137,132,133,232,231,233,228,229,230,124,123,125,120,121,122,159,158,160,161,156,157,163,162,164,165,166,167,169,168,170,171,172,173,128,127,129,130,131,126,4,3,5,1,0,2,179,178,174,175,176,177,279,278,280,281,276,277,483,482,484,486,487,485,597,599,598,596,594,595,600,602,601,603,604,605,477,476,478,479,480,481,362,361,360,363,364,365,453,454,570,455,456,457,463,462,461,460,458,459,465,464,466,467,468,469,535,534,536,538,539,537,551,550,549,548,546,547,641,620,638,637,619,621,651,650,648,649,687,695,670,677,691,683,666,685,680,679,84,85,86,87,88,89,76,75,77,72,73,74,78,83,79,80,81,82,102,107,103,104,105,106,68,67,69,70,71,66,64,63,65,60,61,62,119,116,115,114,117,118,91,90,92,93,94,95,244,243,245,240,241,242,217,216,218,219,220,221,591,593,592,368,366,367,451,450,452,447,448,449,427,426,428,424,425,423,310,309,311,307,306,308,331,330,332,335,333,334,323,322,321,320,318,319,349,348,350,352,353,351,315,317,316,314,312,313,435,437,436,438,439,440,399,401,400,402,403,404,642,652,653,654,655,645,646,643,647,644,662,664,656,660,665,663,657,659,658,661 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#b1cd85d3b2010871ff4296ca3922edaff9632ccb3821306d9c0360a13ac5958c, M = {24, 25, 26, 27, 28, 29, 136} 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 20:23:33 · history