Equation 677 Database

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Magma baa810bdc6bc…

magma baa810bdc6bc
Size
707
Isomorphism class hash
baa810bdc6bc75f375d434f41a81d9f5912f87bf99737352503a763a7acadd59
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
2026-10-06 20:34:31
Display reorder
539,538,540,536,537,535,628,44,43,45,46,47,42,48,50,49,52,53,51,127,126,128,129,130,131,250,249,251,247,246,248,120,125,121,122,123,124,133,132,134,135,136,137,244,243,245,241,240,242,9,8,10,11,6,7,36,41,37,38,39,40,80,79,81,82,83,78,304,303,305,301,300,302,369,371,370,366,367,368,341,340,339,336,337,338,465,464,466,469,467,468,494,496,495,499,497,498,388,387,389,385,386,384,374,373,372,376,377,375,380,379,378,382,383,381,592,591,593,594,595,596,589,588,590,598,439,438,612,643,613,611,610,609,622,645,647,699,671,682,700,675,696,698,689,702,705,706,89,88,84,85,86,87,141,143,142,139,140,138,76,75,77,72,73,74,17,16,12,13,14,15,196,195,197,192,193,194,235,234,236,237,238,239,297,296,298,299,294,295,289,288,290,291,292,293,165,164,166,167,162,163,28,27,29,24,25,26,21,20,22,23,18,19,447,446,448,450,451,449,453,452,454,457,455,456,393,395,394,391,392,390,361,360,362,363,364,365,459,458,460,462,463,461,404,403,402,406,407,405,399,401,400,398,396,397,576,577,578,579,580,581,343,342,344,345,346,347,637,614,615,616,649,648,626,642,625,676,678,695,681,660,667,674,666,677,686,697,275,274,270,271,272,273,62,64,63,60,61,65,55,54,56,57,58,59,283,282,284,285,286,287,226,225,227,222,223,224,265,264,266,267,268,269,114,119,115,116,117,118,210,215,211,212,213,214,66,71,67,68,69,70,278,277,279,280,281,276,220,219,221,216,217,218,564,566,565,567,568,569,415,414,416,419,417,418,442,441,440,443,444,445,505,507,506,510,508,509,412,411,413,409,410,408,605,604,603,601,602,600,544,546,545,543,541,542,512,511,513,514,515,516,552,551,550,548,549,547,627,646,623,644,606,618,608,617,624,694,679,688,693,659,665,684,658,691,685,701,200,199,201,202,203,198,148,144,149,146,147,145,1,5,0,2,3,4,309,308,310,311,306,307,173,172,168,169,170,171,313,312,314,315,316,317,256,255,257,252,253,254,229,228,230,231,232,233,262,261,263,258,259,260,153,152,154,155,150,151,34,33,35,30,31,32,421,420,422,424,425,423,519,518,517,520,521,522,528,527,526,523,524,525,435,437,436,434,432,433,348,350,349,351,352,353,575,574,573,570,572,571,534,533,532,530,531,529,330,331,332,333,334,335,493,492,491,489,490,488,639,620,621,607,638,619,640,651,650,703,668,683,704,661,672,680,657,687,690,692,157,156,158,159,160,161,186,188,187,190,191,189,106,105,101,102,103,104,110,109,111,112,113,108,326,328,327,324,325,329,206,205,207,208,209,204,185,184,180,181,182,183,322,321,323,319,318,320,98,97,99,100,95,96,90,94,107,91,92,93,178,177,179,174,175,176,358,357,359,355,356,354,503,502,504,501,500,599,585,587,586,583,584,582,471,470,472,473,474,475,562,597,563,559,560,561,556,558,557,555,553,554,487,486,485,483,484,482,476,478,477,481,479,480,428,427,426,430,431,429,641,632,631,629,636,633,635,630,634,669,656,663,670,653,654,655,652,662,664,673 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#20e9cec11ce1b4ef3a4be2ce0eb77a027f26009c155c08499f343b203c8ba1b3, M = {108, 109, 110, 111, 112, 113, 128} 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 2026-10-06 20:34:32 · history