Equation 677 Database

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Magma bbf72a6c38d7…

magma bbf72a6c38d7
Size
705
Isomorphism class hash
bbf72a6c38d7f97e2089fae5429b640f3c7db71e6d4e9ba12f93ebad586dab07
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 15:17:54
Display reorder
660,589,620,369,613,596,370,590,614,597,621,371,619,591,615,595,588,368,616,612,592,586,366,617,610,593,587,367,618,611,594,580,375,626,604,602,581,376,627,605,603,582,377,625,606,601,374,583,622,607,598,372,584,623,608,599,373,585,624,609,600,687,688,686,685,416,409,225,449,436,226,414,447,437,410,227,408,415,448,435,419,224,412,445,432,417,222,413,446,433,418,223,411,444,434,422,231,407,440,427,420,232,405,438,428,421,233,406,439,426,230,425,403,443,430,228,423,404,441,431,229,424,402,442,429,703,704,701,702,579,558,47,551,91,48,577,552,92,556,49,557,578,550,90,575,46,561,554,94,576,44,559,555,95,574,45,560,553,93,570,53,564,549,97,568,54,562,547,98,569,55,563,548,96,52,573,567,545,100,50,571,565,546,101,51,572,566,544,99,671,672,670,669,256,238,451,273,267,452,257,274,268,239,450,237,255,275,269,252,454,234,272,266,253,455,235,270,264,254,453,236,271,265,247,457,244,279,258,248,458,245,280,259,246,456,243,281,260,460,250,240,278,261,461,251,241,276,262,459,249,242,277,263,679,680,678,677,507,490,293,474,469,291,508,475,470,491,292,489,509,476,468,506,289,486,477,472,504,290,487,478,473,505,288,488,479,471,498,284,496,480,467,499,282,497,481,465,500,283,495,482,466,287,501,492,483,463,285,502,493,484,464,286,503,494,485,462,692,691,690,689,346,338,530,74,364,528,347,75,365,336,529,337,345,76,363,342,533,341,77,360,343,531,339,78,361,344,532,340,79,362,352,525,333,72,355,353,526,334,73,356,351,527,335,71,354,524,348,332,68,358,522,349,330,69,359,523,350,331,70,357,699,700,698,697,152,149,113,136,116,111,150,137,114,147,112,148,151,135,115,155,109,145,132,119,153,110,146,133,117,154,108,144,134,118,158,104,140,127,122,156,102,138,128,120,157,103,139,126,121,107,161,143,130,125,105,159,141,131,123,106,160,142,129,124,663,664,662,661,642,635,171,30,384,172,640,31,385,636,173,634,641,32,386,645,170,638,29,387,643,168,639,27,388,644,169,637,28,389,648,162,633,21,382,646,163,631,22,383,647,164,632,23,381,165,651,629,24,378,166,649,630,25,379,167,650,628,26,380,682,683,684,681,39,541,11,12,87,9,40,13,88,542,10,540,41,14,86,42,7,543,43,89,652,8,654,653,655,656,6,659,657,658,37,2,539,15,85,38,1,537,16,83,36,0,538,17,84,5,33,535,18,81,3,34,536,19,82,4,35,534,20,80,695,696,693,694,301,59,515,323,306,513,302,321,307,60,514,61,300,322,308,304,511,58,319,309,305,512,56,320,310,303,510,57,318,311,299,521,65,329,312,297,519,66,327,313,298,520,67,328,314,517,295,64,325,315,518,296,62,326,316,516,294,63,324,317,667,668,665,666,186,177,396,210,201,397,187,211,202,178,398,179,188,212,203,189,399,176,213,200,190,400,174,214,198,191,401,175,215,199,192,394,183,216,207,193,395,184,217,208,194,393,185,218,209,390,195,182,219,206,391,196,180,220,204,392,197,181,221,205,675,676,673,674 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*64, 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, 11, B) with E = magma#11540e60a31227d97822464caf7bd085f23c491501101f6992da34196185b51e, M = {60} in E, B = magma#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39. 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(11, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + 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: 45.

last edited by qawbecrdtey at 2026-10-03 15:17:57 · history