Equation 677 Database

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Magma a8a77d543e8d…

magma a8a77d543e8d
Size
705
Isomorphism class hash
a8a77d543e8db1df92b19ddde0a406d5f0c1e59d0267738240b0c82a4c290be7
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 16:56:18
Display reorder
660,142,355,115,364,125,143,356,116,365,123,141,354,114,363,124,138,358,118,360,121,139,359,119,361,122,140,357,117,362,120,133,353,113,370,131,134,351,111,371,129,132,352,112,369,130,349,136,109,366,127,350,137,110,367,128,348,135,108,368,126,685,686,688,687,440,223,249,231,21,438,224,250,232,22,439,222,251,233,23,443,226,248,230,20,441,227,246,228,18,442,225,247,229,19,435,221,240,237,12,436,219,241,238,13,437,220,242,239,14,217,434,243,236,15,218,432,244,234,16,216,433,245,235,17,701,702,704,703,344,567,541,585,562,342,568,542,586,563,343,569,540,587,561,347,566,544,584,558,345,564,545,582,559,346,565,543,583,560,339,573,547,576,553,340,574,548,577,554,341,575,546,578,552,572,338,550,579,556,570,336,551,580,557,571,337,549,581,555,670,669,672,671,449,260,277,264,202,447,258,278,265,203,448,259,276,266,201,445,263,280,267,198,446,261,281,268,199,444,262,279,269,200,455,255,283,270,193,453,256,284,271,194,454,257,282,272,192,254,451,286,273,196,252,452,287,274,197,253,450,285,275,195,680,677,679,678,457,210,151,294,174,458,211,152,295,175,456,212,150,296,176,460,213,154,297,177,461,214,155,298,178,459,215,153,299,179,463,208,149,292,172,464,209,147,293,173,462,207,148,291,171,204,466,145,288,168,205,467,146,289,169,206,465,144,290,170,689,690,691,692,7,316,65,100,498,8,317,63,101,499,6,315,64,99,500,10,312,61,96,501,11,313,62,97,502,9,314,60,98,503,5,322,71,106,496,3,323,69,107,497,4,321,70,105,495,318,0,67,102,492,319,2,68,103,493,320,1,66,104,494,697,698,700,699,599,623,647,627,603,597,621,645,628,604,598,622,646,629,605,595,619,643,626,602,596,620,644,624,600,594,618,642,625,601,590,614,638,633,609,588,612,636,634,610,589,613,637,635,611,617,593,641,632,608,615,591,639,630,606,616,592,640,631,607,661,662,664,663,43,26,79,380,87,44,24,80,378,88,42,25,78,379,89,46,29,82,383,86,47,27,83,381,84,45,28,81,382,85,41,32,77,375,93,39,30,75,376,94,40,31,76,377,95,35,37,73,374,92,33,38,74,372,90,34,36,72,373,91,682,681,684,683,331,508,529,518,534,332,509,530,516,535,330,507,528,517,536,334,511,525,514,533,335,512,526,515,531,333,510,527,513,532,329,652,654,653,655,327,657,658,656,659,328,648,650,649,651,505,325,523,520,539,506,326,524,521,537,504,324,522,519,538,693,694,696,695,180,162,482,476,300,181,163,480,474,301,182,164,481,475,302,183,165,485,479,303,184,166,483,477,304,185,167,484,478,305,186,160,488,471,306,187,161,486,472,307,188,159,487,473,308,156,189,491,470,309,157,190,489,468,310,158,191,490,469,311,666,665,668,667,52,419,394,423,399,53,417,395,424,400,51,418,393,425,401,48,415,390,422,398,49,416,391,420,396,50,414,392,421,397,58,410,385,429,405,59,408,386,430,406,57,409,384,431,407,413,54,388,428,404,411,55,389,426,402,412,56,387,427,403,674,673,676,675 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#49acd73e7fb20809c4c5aee6104079a0019ec0e0539c0b91c35b8b4466bd197d, 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 16:56:19 · history