Equation 677 Database

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Magma fa7002a30b75…

magma fa7002a30b75
Size
707
Isomorphism class hash
fa7002a30b75a36b94d22bf25b34e8f41f9e94fece455ec62848936d5b295117
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 00:25:15
Display reorder
331,335,330,332,333,334,706,322,319,323,320,321,318,89,88,84,85,86,87,198,203,199,200,201,202,98,97,99,100,101,96,121,120,122,123,124,125,172,171,173,168,169,170,163,162,164,165,166,167,290,289,293,291,288,292,296,294,297,298,299,295,329,328,326,327,325,324,160,159,161,156,157,158,579,581,580,578,577,576,450,452,451,453,454,455,509,508,507,504,505,506,485,484,483,480,481,482,473,472,471,470,468,469,496,495,497,492,493,494,575,574,573,571,572,570,345,347,346,342,343,344,390,392,391,395,393,394,612,609,607,608,610,611,633,606,620,670,677,664,691,694,699,702,700,701,705,704,59,55,54,57,58,56,276,281,277,278,279,280,14,13,15,16,17,12,267,266,268,269,264,265,213,212,214,215,210,211,25,24,26,27,28,29,31,30,32,33,34,35,67,66,68,69,70,71,65,64,60,61,62,63,235,234,236,237,238,239,242,241,243,244,245,240,535,534,536,537,538,539,514,513,515,511,512,510,368,367,366,369,370,371,430,429,431,428,426,427,601,602,600,603,604,605,425,424,423,421,422,420,398,397,396,400,401,399,567,569,568,564,565,566,563,562,561,559,560,558,622,624,625,627,626,628,631,623,629,654,683,675,665,680,676,682,692,681,697,703,149,145,144,147,148,146,132,137,133,134,135,136,285,284,286,287,282,283,151,150,152,153,154,155,310,309,311,307,306,308,220,219,221,216,217,218,301,305,300,302,303,304,74,73,75,76,77,72,81,80,82,83,78,79,205,204,206,207,208,209,272,271,273,274,275,270,589,590,588,593,591,592,523,522,524,526,527,525,351,353,352,349,350,348,587,586,585,583,582,584,530,529,528,533,531,532,383,382,381,379,380,378,375,377,376,374,372,373,385,384,386,388,389,387,594,595,596,597,598,599,613,619,617,616,618,614,632,630,621,663,689,679,678,667,666,685,668,690,686,698,47,43,42,45,46,44,139,138,140,141,142,143,231,230,232,233,228,229,41,40,36,37,38,39,222,227,223,224,225,226,247,246,248,249,250,251,255,254,256,257,252,253,19,18,20,21,22,23,262,261,263,258,259,260,315,314,316,317,313,312,48,53,49,50,51,52,358,357,359,354,355,356,362,361,360,365,363,364,411,413,412,409,410,408,406,405,407,404,402,403,557,556,555,554,552,553,550,549,551,546,547,548,416,415,414,418,419,417,516,518,517,519,520,521,541,540,542,543,544,545,645,642,640,643,641,644,634,615,635,688,673,662,693,674,672,687,671,684,695,696,194,196,195,192,193,197,188,187,189,190,191,186,185,184,180,181,182,183,6,11,7,8,9,10,110,109,111,112,113,108,115,114,116,117,118,119,106,105,107,102,103,104,1,5,0,2,3,4,90,95,91,92,93,94,174,179,175,176,177,178,129,128,130,131,126,127,464,463,462,466,467,465,341,340,339,338,337,336,448,447,449,446,444,445,479,478,477,474,475,476,487,486,488,490,491,489,500,499,498,502,503,501,456,458,457,461,459,460,433,432,434,436,437,435,440,439,438,442,443,441,648,650,637,649,646,647,639,638,636,653,655,652,656,658,651,659,660,657,661,669 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#51f9b7d09d33f9fd9b24ec352fcf17309682f23da1a55124c3f963e5739f1055, M = {6, 7, 8, 9, 10, 11, 138} 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 00:25:20 · history