Equation 677 Database

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Magma b4cb61278fe7…

magma b4cb61278fe7
Size
707
Isomorphism class hash
b4cb61278fe769ac1674ef8fe5de0a1aade3e488635beb0664a61b0020c5ef99
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
2026-10-08 22:01:55
Display reorder
602,603,604,605,601,600,706,586,578,596,563,149,542,575,128,154,161,112,548,569,125,590,538,136,118,142,587,591,579,597,559,144,543,570,129,155,156,113,549,564,120,143,534,137,119,582,592,580,598,558,145,544,571,130,150,157,108,550,565,121,138,535,132,114,583,593,581,599,560,146,545,572,131,151,158,109,551,566,122,139,536,133,115,584,588,576,594,561,147,541,573,126,152,159,110,547,567,123,140,537,134,116,585,589,577,595,562,148,540,574,127,153,160,111,546,568,124,141,539,135,117,552,555,556,557,553,554,628,630,629,627,626,631,703,700,701,705,702,704,699,655,659,654,658,653,657,656,237,309,56,216,63,27,484,424,389,191,202,419,166,430,30,39,295,169,223,238,31,310,57,217,64,28,485,425,384,186,203,414,167,431,224,40,296,170,239,32,311,58,218,65,29,480,420,385,187,198,415,162,426,225,41,297,171,234,33,306,59,219,60,24,481,421,386,188,199,416,163,427,226,36,298,172,235,34,307,54,220,61,25,482,422,387,189,200,417,164,428,227,37,299,173,236,35,308,55,221,62,26,483,423,388,190,201,418,165,429,222,38,294,168,193,195,196,197,192,194,677,676,673,674,675,672,652,651,647,649,650,637,648,683,684,679,680,678,681,682,88,490,292,400,322,412,44,443,262,269,66,404,325,95,314,52,96,240,392,89,315,491,293,401,323,413,45,438,263,264,67,405,326,90,393,53,97,241,84,316,487,288,396,318,408,46,439,258,265,68,406,327,91,394,48,98,242,85,317,486,289,397,319,409,47,440,259,266,69,407,328,92,395,49,99,243,86,312,488,290,398,320,410,42,441,260,267,70,402,329,93,390,50,100,244,87,313,489,291,399,321,411,43,442,261,268,71,403,324,94,391,51,101,245,275,271,272,273,274,270,664,662,665,669,668,661,645,639,640,642,641,646,633,686,691,694,690,688,698,696,228,508,502,364,382,520,352,496,479,533,436,467,461,455,181,179,301,344,212,229,182,509,503,365,383,521,353,497,474,528,437,462,456,450,213,174,302,345,230,183,504,498,360,378,516,348,492,475,529,432,463,457,451,214,175,303,346,231,184,505,499,361,379,517,349,493,476,530,433,464,458,452,215,176,304,347,232,185,506,500,362,380,518,350,494,477,531,434,465,459,453,210,177,305,342,233,180,507,501,363,381,519,351,495,478,532,435,466,460,454,211,178,300,343,4,1,0,2,3,5,671,663,666,670,667,660,632,643,636,644,634,638,635,695,693,697,692,687,685,689,340,80,281,370,284,107,77,20,254,208,251,17,10,332,449,354,522,468,372,341,445,81,276,371,285,102,72,21,255,209,246,12,11,333,373,355,523,469,336,444,82,277,366,286,103,73,22,256,204,247,13,6,334,374,356,524,470,337,446,83,278,367,287,104,74,23,257,205,248,14,7,335,375,357,525,471,338,447,78,279,368,282,105,75,18,252,206,249,15,8,330,376,358,526,472,339,448,79,280,369,283,106,76,19,253,207,250,16,9,331,377,359,527,473,512,514,515,510,511,513,624,614,620,615,622,616,619,609,621,618,625,623,617,610,606,613,607,608,611,612 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#ab7663272fb322647e3a6f8af752cc36283f2dfca26817d870d65fdaf95a91e5, M = {8, 29, 49, 69, 89, 109, 127} 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 2026-10-08 22:01:56 · history