Equation 677 Database

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Magma bc8f35d5e794…

magma bc8f35d5e794
Size
707
Isomorphism class hash
bc8f35d5e7941bd573380e92696fab1a1f183db36ce3e72caa06fc117ec4d167
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 09:43:00
Display reorder
471,470,466,467,468,469,680,171,173,169,170,168,172,162,164,163,165,166,167,205,204,206,209,207,208,305,304,303,300,301,302,153,155,154,152,150,151,156,158,157,159,160,161,214,213,215,212,210,211,252,254,253,256,257,255,293,292,291,288,289,290,297,299,298,294,295,296,308,307,306,311,309,310,472,477,473,474,475,476,517,516,518,519,514,515,512,511,513,508,509,510,334,333,335,330,331,332,520,525,521,522,523,524,349,348,350,351,352,353,410,409,411,412,407,408,563,562,564,565,596,591,593,597,592,595,594,566,656,647,654,657,655,630,632,631,640,639,629,696,706,672,661,705,682,671,667,662,148,147,146,144,145,149,47,46,45,44,42,43,113,112,111,108,109,110,106,105,107,104,102,103,114,116,115,119,117,118,174,176,175,177,178,179,123,125,124,121,122,120,192,194,193,196,197,195,99,101,100,97,98,96,50,49,48,53,51,52,128,127,126,131,129,130,598,601,599,600,526,527,491,490,492,493,494,495,445,444,446,447,442,443,463,462,464,465,460,461,451,450,452,453,448,449,496,501,497,498,499,500,558,557,559,589,590,588,573,576,574,575,548,549,370,369,367,368,366,567,619,637,618,625,610,633,628,609,624,620,621,695,683,669,666,686,699,690,674,691,81,83,79,80,78,82,7,6,8,10,11,9,56,55,54,57,58,59,15,17,16,13,14,12,2,0,1,4,5,3,188,187,186,191,189,190,275,274,273,270,271,272,33,35,34,31,32,30,94,93,95,92,90,91,235,234,236,238,239,237,40,39,41,37,38,36,456,455,457,458,459,454,489,488,484,485,486,487,391,390,392,393,394,389,423,422,424,419,420,421,396,395,397,398,399,400,531,530,532,533,529,528,555,554,556,587,585,586,582,581,583,584,552,553,538,537,539,540,541,572,606,608,617,634,644,636,614,623,651,616,622,697,687,676,664,689,698,694,665,693,218,217,219,220,221,216,244,243,245,241,242,240,263,262,261,258,259,260,66,67,68,71,69,70,315,317,316,314,313,312,225,227,226,222,223,224,61,62,60,64,65,63,76,75,77,74,73,72,276,278,277,280,281,279,132,134,133,135,136,137,140,139,138,143,141,142,602,605,603,604,560,561,378,377,379,380,381,382,403,402,404,405,406,401,430,429,425,426,427,428,375,374,376,371,372,373,543,547,542,544,545,546,534,535,536,571,570,569,578,577,579,580,550,551,438,437,439,440,441,568,613,612,652,627,626,642,641,645,611,649,658,692,681,678,679,688,677,685,700,684,202,201,200,198,199,203,182,181,180,185,183,184,327,329,328,325,326,324,84,86,85,88,89,87,320,319,318,322,323,321,287,286,285,284,282,283,246,248,247,250,251,249,228,230,229,232,233,231,266,265,264,267,268,269,18,20,19,21,22,23,26,25,24,29,27,28,355,354,356,357,358,359,436,435,431,432,433,434,339,338,340,341,336,337,386,385,387,388,383,384,345,344,346,347,342,343,363,362,364,365,360,361,505,504,506,507,502,503,479,478,480,481,482,483,418,417,413,414,415,416,615,643,650,648,607,653,638,635,646,660,659,670,673,701,704,668,675,663,703,702 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 = {72, 73, 74, 75, 76, 77, 139} 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 09:43:01 · history