Equation 677 Database

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Magma 1a518af140e5…

magma 1a518af140e5
Size
707
Isomorphism class hash
1a518af140e5e707bfc658f34881554826699f22de59538db25f55df18641bde
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 19:16:55
Display reorder
475,474,473,476,477,478,638,179,181,182,183,184,180,80,79,81,82,83,78,77,76,72,73,74,75,318,319,320,321,322,323,208,207,209,210,211,212,152,151,153,154,155,150,270,275,271,272,273,274,280,279,281,276,277,278,239,238,234,235,236,237,329,328,326,327,325,324,269,268,264,265,266,267,519,518,517,515,516,514,386,385,384,388,389,387,339,341,340,337,338,336,440,442,441,438,439,437,529,531,530,527,528,526,540,539,538,541,542,543,557,558,559,560,562,561,402,404,403,405,406,407,509,511,510,512,563,513,610,613,612,614,609,611,622,621,634,679,681,691,688,697,706,698,703,690,704,705,257,253,254,255,256,252,86,85,87,88,89,84,99,98,100,101,96,97,195,194,190,191,192,193,60,65,61,62,63,64,306,307,308,309,310,311,34,33,35,30,31,32,317,316,313,312,314,315,38,37,39,40,41,36,58,57,59,54,55,56,24,29,25,26,27,28,413,415,414,418,416,417,372,374,373,377,375,376,583,584,582,586,587,585,590,588,589,591,592,593,578,576,577,579,580,581,489,490,488,485,486,487,574,573,575,571,570,572,363,365,364,360,361,362,508,507,506,505,503,504,626,624,627,623,629,628,625,630,632,662,693,702,669,683,695,670,694,661,674,701,22,18,19,20,21,23,15,14,16,17,12,13,8,7,9,10,11,6,122,121,123,124,125,120,5,4,1,0,2,3,251,250,246,247,248,249,71,70,66,67,68,69,262,261,263,258,259,260,178,177,173,174,175,176,146,145,147,148,149,144,93,92,94,95,90,91,472,471,470,468,469,467,391,390,392,393,394,395,398,397,396,399,400,401,358,357,359,356,354,355,420,419,421,424,422,423,569,568,567,564,565,566,411,410,412,544,408,409,445,444,443,448,446,447,366,368,367,369,370,371,608,607,617,606,618,619,620,631,633,668,689,699,680,671,687,672,676,663,665,696,45,47,42,43,44,46,141,140,142,143,138,139,49,48,50,51,52,53,111,110,112,113,108,109,136,135,137,132,133,134,289,288,290,291,292,293,304,303,305,300,301,302,285,284,286,287,282,283,107,106,102,103,104,105,126,131,127,128,129,130,114,119,115,116,117,118,596,594,595,598,599,597,493,492,491,495,496,494,465,464,466,463,461,462,602,600,601,603,604,605,502,501,500,497,498,499,481,480,479,482,483,484,551,553,552,556,554,555,453,452,454,450,451,449,459,458,460,456,457,455,646,643,641,644,642,645,637,635,636,686,682,692,700,673,685,678,675,664,677,684,205,201,202,203,204,206,298,297,299,294,295,296,167,172,168,169,170,171,199,198,220,200,196,197,225,224,226,227,222,223,166,219,163,164,165,162,230,229,231,232,233,228,185,218,186,187,188,189,241,240,242,243,244,245,217,216,221,213,214,215,156,161,157,158,159,160,349,348,350,351,352,353,536,535,537,532,533,534,381,383,382,379,380,378,435,434,436,433,431,432,430,429,428,425,426,427,346,345,347,344,342,343,335,334,333,330,332,331,545,547,546,548,549,550,520,522,521,523,524,525,649,651,615,650,647,648,639,616,640,654,659,667,658,656,660,655,657,652,653,666 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#e4013d0178842fa1abe6ac84eb6d8732370ca50237187a2a953024cf339ab2c2, M = {72, 73, 74, 75, 76, 77, 133} 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 19:16:56 · history