Equation 677 Database

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Magma 6c3f3a4a86c9…

magma 6c3f3a4a86c9
Size
707
Isomorphism class hash
6c3f3a4a86c954363d34a769241c72b3eeaa744de608d76f77b44572ac2b2eff
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 01:51:50
Display reorder
168,170,169,172,173,171,656,149,148,144,145,146,147,226,225,227,223,224,222,281,280,279,277,276,278,236,235,234,237,238,239,272,270,271,274,275,273,246,248,247,249,250,251,232,231,233,230,228,229,20,19,18,21,22,23,111,113,112,108,109,110,303,305,304,301,300,302,391,390,392,393,394,395,332,331,333,334,335,330,337,336,338,339,340,341,547,546,548,549,550,551,514,513,515,510,511,512,346,345,347,342,343,344,603,602,604,605,600,601,574,573,575,570,571,572,498,503,499,500,501,502,595,594,596,597,598,599,612,620,613,607,609,621,652,619,633,647,692,704,676,674,675,673,693,686,660,706,45,47,43,44,42,46,65,64,63,62,60,61,205,204,206,209,207,208,58,57,59,56,54,55,160,159,161,156,157,158,212,211,210,215,213,214,52,51,53,50,48,49,37,36,38,41,39,40,130,129,131,127,128,126,243,245,244,241,240,242,526,525,527,522,523,524,518,517,519,520,521,516,400,399,401,396,397,398,439,438,440,441,442,443,490,489,491,486,487,488,562,561,563,558,559,560,494,493,495,496,497,492,540,545,541,542,543,544,309,308,310,311,307,306,469,468,470,471,472,473,638,655,636,630,640,650,649,616,629,642,689,667,668,658,672,657,683,659,671,662,25,24,29,27,28,26,15,17,16,12,13,14,263,262,261,259,258,260,30,32,31,34,35,33,254,252,253,256,257,255,221,220,219,218,216,217,183,185,184,181,182,180,155,154,153,150,151,152,124,123,125,121,122,120,195,197,196,192,193,194,312,317,313,314,315,316,319,318,320,321,322,323,564,569,565,566,567,568,362,361,363,364,365,360,355,354,356,357,358,359,577,576,578,579,580,581,508,507,509,504,505,506,371,370,366,367,368,369,403,402,404,405,406,407,409,408,410,411,412,413,645,653,641,627,639,651,646,615,631,632,694,684,665,691,666,681,679,687,663,680,67,66,71,69,70,68,115,114,116,118,119,117,90,92,91,94,95,93,191,190,189,186,187,188,98,97,96,100,101,99,266,265,264,269,267,268,9,11,10,7,8,6,165,167,166,163,164,162,5,4,3,2,1,0,199,198,200,202,203,201,325,324,326,327,328,329,353,352,348,349,350,351,535,534,536,537,538,539,531,530,532,533,528,529,474,479,475,476,477,478,444,449,445,446,447,448,451,450,452,453,454,455,552,557,553,554,555,556,389,388,384,385,386,387,435,434,436,437,432,433,644,648,643,628,635,654,637,618,625,626,670,685,669,682,664,661,688,690,678,677,81,83,79,80,78,82,134,133,132,137,135,136,282,283,284,287,285,286,88,87,89,86,84,85,106,105,107,102,103,104,143,142,141,140,138,139,289,290,288,292,293,291,178,177,179,176,174,175,75,77,76,72,73,74,299,298,297,296,295,294,377,376,372,373,374,375,414,419,415,416,417,418,460,459,461,456,457,458,380,379,381,382,383,378,420,425,421,422,423,424,426,431,427,428,429,430,592,591,593,588,589,590,466,465,467,462,463,464,482,481,483,484,485,480,583,587,582,584,585,586,614,622,611,606,608,624,634,610,623,617,701,703,699,700,702,695,697,696,698,705 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#141a5ad98d093a51cbcd8d0e5f762ac857a7d54b6447f4e2b6939d4d1af2e3e9, M = {36, 37, 38, 39, 40, 41, 134} 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 01:51:51 · history