Equation 677 Database

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Magma c0b49412beae…

magma c0b49412beae
Size
707
Isomorphism class hash
c0b49412beae7f10178640f1af053982781a357c23d60ae8736459c29dd1edac
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 08:10:30
Display reorder
305,304,303,301,300,302,656,220,219,218,216,217,221,191,190,189,186,187,188,182,181,180,185,183,184,244,243,245,242,240,241,16,15,17,14,12,13,89,88,87,84,85,86,127,126,128,130,131,129,251,250,249,248,246,247,133,132,134,135,136,137,193,192,194,196,197,195,400,405,401,402,403,404,326,325,327,328,329,324,436,441,437,438,439,440,597,596,592,593,594,595,354,353,355,356,357,352,348,347,349,350,351,346,310,309,311,307,306,308,399,398,394,395,396,397,572,571,573,568,569,570,387,386,382,383,384,385,618,619,606,621,607,610,645,617,636,638,701,681,675,703,660,657,659,702,691,700,262,261,260,258,259,263,257,256,255,252,253,254,48,50,49,51,52,53,28,27,29,26,24,25,45,47,46,43,44,42,238,237,239,236,234,235,206,205,204,209,207,208,8,7,6,11,9,10,93,95,94,92,90,91,98,97,96,101,99,100,368,367,369,364,365,366,377,376,378,379,380,381,565,564,566,567,562,563,340,345,341,342,343,344,531,530,526,527,528,529,534,533,535,536,537,532,555,554,550,551,552,553,461,460,462,463,464,465,500,499,501,496,497,498,442,447,443,444,445,446,653,649,626,647,632,642,639,613,641,644,676,664,682,662,679,661,672,670,667,671,273,275,270,272,271,274,35,34,33,30,31,32,105,107,106,102,103,104,280,279,281,278,277,276,286,285,287,284,283,282,268,267,269,266,265,264,111,113,112,108,109,110,203,202,201,200,198,199,62,61,60,64,65,63,67,66,68,70,71,69,432,431,433,434,435,430,587,586,588,589,590,602,583,582,584,585,580,581,574,579,575,576,577,578,542,541,543,538,539,540,598,601,605,604,599,600,591,603,336,337,338,339,388,393,389,390,391,392,521,520,522,523,524,525,472,477,473,474,475,476,655,654,631,652,633,640,635,620,646,634,685,683,674,688,689,690,692,687,684,686,72,74,76,77,75,73,179,178,177,174,175,176,83,82,81,80,78,79,222,224,223,226,227,225,231,233,232,229,230,228,119,118,117,114,115,116,56,54,55,59,57,58,122,121,120,125,123,124,23,22,21,19,20,18,37,36,38,40,41,39,359,358,360,361,362,363,332,331,333,334,335,330,515,514,516,517,518,519,557,556,558,559,560,561,466,471,467,468,469,470,509,508,510,511,512,513,373,372,374,375,370,371,454,459,455,456,457,458,547,546,548,549,544,545,450,449,451,452,453,448,651,648,629,650,625,637,630,614,643,628,677,680,658,665,669,673,668,663,678,666,294,295,299,297,298,296,149,148,147,144,145,146,139,138,140,142,143,141,211,210,212,215,213,214,0,1,2,5,3,4,288,289,290,293,291,292,152,151,150,155,153,154,159,161,160,156,157,158,167,166,165,163,164,162,171,173,172,168,169,170,319,318,320,321,322,323,314,313,315,316,317,312,491,490,492,493,494,495,503,502,504,505,506,507,484,489,485,486,487,488,481,480,482,483,478,479,426,425,427,428,429,424,421,420,422,423,418,419,406,411,407,408,409,410,414,413,415,416,417,412,622,616,609,615,608,611,623,612,627,624,706,698,693,696,699,704,695,705,694,697 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#ca4e87f44b5aa8ee937e3111d7e18929d38c701d18b6266af0f19751e7c29bcd, M = {6, 7, 8, 9, 10, 11, 131} 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 08:10:31 · history