Equation 677 Database

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Magma bce675c0b00b…

magma bce675c0b00b
Size
707
Isomorphism class hash
bce675c0b00bc0cf5b0aba186e9c8bdc80112cade7e9cc468cdbb44e57d14693
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 14:17:41
Display reorder
601,600,602,603,604,605,706,594,62,554,562,540,66,530,92,571,586,77,55,569,579,588,549,78,51,538,595,589,60,553,563,542,67,529,90,572,587,75,56,567,580,550,79,539,52,596,590,61,552,561,541,68,528,91,570,585,76,54,568,581,551,80,537,53,533,544,95,574,583,74,58,566,576,591,597,65,557,558,69,48,534,81,547,70,545,531,93,575,584,72,59,565,577,592,598,63,555,560,49,536,546,82,543,532,71,94,573,582,73,57,564,578,593,599,64,556,559,548,50,535,83,524,523,526,527,525,522,672,674,673,675,677,676,632,627,629,630,626,628,631,702,705,700,701,704,703,699,141,517,498,506,357,352,492,481,301,172,510,490,47,3,156,130,245,376,431,142,157,516,499,504,358,353,493,480,300,173,511,491,45,4,131,243,429,377,143,158,518,500,505,359,351,494,482,302,171,512,489,46,5,129,244,430,375,495,355,483,303,169,513,487,44,1,159,138,519,501,509,348,372,428,242,127,350,354,496,484,304,170,514,488,42,0,160,139,520,502,507,374,427,128,240,356,497,349,485,305,168,515,486,43,2,161,140,521,503,508,126,373,426,241,369,370,368,367,366,371,633,645,647,635,636,637,696,693,692,694,698,697,695,652,653,663,654,651,664,655,312,202,333,40,475,466,25,227,23,236,322,189,308,206,9,448,455,457,440,314,10,203,334,41,476,467,26,225,21,234,323,190,307,204,449,453,439,458,313,11,201,335,39,474,465,24,226,22,235,321,191,306,205,447,454,438,456,28,478,224,20,239,318,186,311,209,6,316,199,331,37,463,460,443,452,445,464,479,29,222,18,237,320,187,309,207,7,317,200,330,38,461,441,446,450,477,27,462,223,19,238,319,188,310,208,8,315,198,332,36,444,459,442,451,471,472,470,468,469,473,650,642,648,649,644,643,683,679,682,678,684,680,681,665,668,671,667,670,669,666,211,380,360,338,403,399,232,346,299,14,437,327,221,32,185,386,408,393,420,212,183,379,362,337,404,400,233,347,296,12,435,328,219,30,385,409,422,394,210,184,378,361,336,402,401,231,345,294,13,436,329,220,31,384,410,421,395,229,406,342,295,17,434,325,218,35,182,214,383,364,341,396,390,424,411,389,397,407,230,344,297,15,433,324,216,33,180,215,381,365,339,391,425,387,412,405,228,398,343,298,16,432,326,217,34,181,213,382,363,340,388,392,423,413,417,418,416,414,415,419,641,646,638,634,639,640,687,686,688,691,685,689,690,659,660,662,657,658,656,661,288,122,108,276,84,132,106,163,98,286,148,268,256,196,179,118,150,263,248,290,177,120,109,278,85,133,107,164,96,287,149,269,257,197,119,151,246,261,289,178,121,110,277,86,134,105,162,97,285,147,267,255,195,117,152,247,262,103,87,166,101,282,145,264,252,193,176,292,125,111,280,135,260,251,153,115,136,88,104,167,99,284,146,266,254,194,174,293,123,112,281,259,249,116,154,89,102,137,165,100,283,144,265,253,192,175,291,124,113,279,114,258,250,155,273,274,272,271,270,275,613,607,625,617,623,624,621,609,612,620,615,619,606,610,616,618,608,614,611,622 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#a8026a02368cc98eace7a76910bb242dec082e21ec6371f1fc7226b87fb07666, M = {4, 25, 45, 74, 95, 115, 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 2026-10-07 14:17:43 · history