Equation 677 Database

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Magma a1920226cea4…

magma a1920226cea4
Size
707
Isomorphism class hash
a1920226cea4cfa542356aadc585a888326e3180525072cf08764ab08db1f7f7
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 14:23:53
Display reorder
528,527,526,531,529,530,632,30,35,31,32,33,34,210,213,211,212,215,214,295,294,296,297,298,299,289,288,290,291,292,293,246,251,247,248,249,250,127,126,128,129,130,125,256,255,257,253,252,254,262,261,263,259,258,260,108,107,109,110,111,112,150,149,151,152,153,154,302,300,303,304,305,301,436,435,434,433,431,432,438,437,439,442,440,441,534,533,535,536,537,538,455,457,456,460,458,459,454,453,452,450,451,449,446,448,447,445,443,444,493,492,491,495,496,494,429,428,430,425,426,427,385,384,386,389,387,388,620,635,616,617,618,621,619,645,647,700,670,682,698,680,697,699,691,703,706,705,157,156,158,159,160,155,120,123,121,122,119,124,117,116,118,113,114,115,145,144,146,147,148,143,82,81,77,78,79,80,60,59,61,62,63,64,99,98,100,95,96,97,88,87,83,84,85,86,104,103,105,106,101,102,6,11,7,8,9,10,93,92,94,89,90,91,559,560,558,561,562,563,366,368,367,370,371,369,381,383,382,380,378,379,374,373,372,376,377,375,466,465,464,462,463,461,337,336,338,339,340,341,515,517,516,520,518,519,590,588,589,592,593,591,567,569,568,565,566,564,614,609,610,615,649,648,642,636,640,679,678,686,675,660,673,668,674,677,687,696,131,136,132,133,134,135,230,233,231,232,229,228,17,16,12,13,14,15,237,236,238,239,234,235,283,282,284,285,286,287,264,269,265,266,267,268,55,54,56,57,58,53,70,69,65,66,67,68,140,139,141,142,137,138,28,27,29,24,25,26,76,75,71,72,73,74,470,472,471,467,468,469,403,402,532,404,405,406,579,581,580,578,577,576,483,482,484,479,480,481,605,604,603,600,602,601,420,419,421,422,423,424,486,485,487,488,489,490,474,473,475,476,477,478,584,582,583,585,586,587,634,646,624,644,633,638,608,641,643,693,683,690,694,661,665,676,657,692,684,701,184,183,179,180,181,182,49,52,50,51,48,47,46,45,41,42,43,44,309,308,310,311,306,307,18,23,19,20,21,22,314,313,315,316,317,312,172,171,167,168,169,170,1,5,0,2,3,4,225,224,226,227,222,223,166,165,161,162,163,164,178,177,173,174,175,176,553,552,551,556,554,555,572,571,570,573,574,575,391,390,392,393,394,395,524,525,557,523,521,522,351,353,352,350,348,349,361,360,362,364,365,363,542,544,543,541,539,540,514,513,512,510,511,509,596,594,595,597,598,599,637,607,612,606,611,613,639,651,650,702,667,681,704,658,669,685,664,689,688,695,196,195,191,192,193,194,218,221,219,220,217,216,204,209,205,206,207,208,201,200,202,197,198,199,326,328,327,324,325,329,38,37,39,36,203,40,186,185,187,188,189,190,321,320,322,323,319,318,244,243,245,240,241,242,280,279,281,276,277,278,270,275,271,272,273,274,354,356,355,357,358,359,347,346,345,342,343,344,546,545,547,548,549,550,412,411,410,408,409,407,498,497,499,500,501,502,504,503,505,506,507,508,332,330,331,334,335,333,398,397,396,400,401,399,415,414,413,416,417,418,627,628,625,629,626,622,631,630,623,671,656,659,666,654,653,655,652,662,663,672 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#3cc60f474fc5309f8bfdc916c4fdc0ad032cdecf3f770b83999110b499ecb4f1, M = {66, 67, 68, 69, 70, 71, 130} 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 14:23:54 · history