Equation 677 Database

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Magma aa61879c9cf1…

magma aa61879c9cf1
Size
705
Isomorphism class hash
aa61879c9cf1d720641aa0edb427515b87762a8d6a0d2e283f3121b78f164106
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 21:12:53
Display reorder
660,285,500,524,245,98,286,522,243,96,498,287,499,523,244,97,284,527,503,241,101,282,525,501,242,99,283,526,502,240,100,530,276,506,251,104,249,528,277,504,102,529,278,505,250,103,279,533,509,247,107,280,531,507,248,105,281,532,508,246,106,662,669,666,667,339,296,221,572,410,340,219,570,408,294,341,295,220,571,409,338,217,299,575,413,336,218,297,573,411,337,216,298,574,412,227,345,291,578,416,576,225,346,292,414,226,347,293,577,415,344,223,290,581,419,342,224,288,579,417,343,222,289,580,418,689,686,691,687,125,65,548,386,49,123,546,384,50,63,124,64,547,385,48,121,551,61,389,52,122,549,62,387,53,120,550,60,388,51,554,131,71,392,55,390,552,129,69,56,553,130,70,391,54,127,557,67,395,58,128,555,68,393,59,126,556,66,394,57,664,672,665,668,237,307,482,560,168,238,480,558,169,308,239,306,481,559,170,236,485,310,563,171,234,483,311,561,172,235,484,309,562,173,488,228,305,566,174,564,486,229,303,175,487,230,304,565,176,231,491,301,569,177,232,489,302,567,178,233,490,300,568,179,682,675,673,679,38,398,191,320,334,36,189,318,335,396,37,397,190,319,333,41,187,401,323,330,39,188,399,321,331,40,186,400,322,332,182,44,404,315,325,316,180,42,402,326,181,43,403,317,324,47,185,407,314,328,45,183,405,312,329,46,184,406,313,327,663,671,661,670,82,446,115,86,602,83,116,84,600,444,81,445,114,85,601,78,118,449,89,605,79,119,447,87,603,80,117,448,88,604,113,73,452,92,608,90,111,74,450,606,112,72,451,91,607,76,109,455,95,611,77,110,453,93,609,75,108,454,94,610,696,699,695,693,34,19,596,496,16,35,594,497,17,20,33,18,595,495,15,30,599,22,492,12,31,597,23,493,13,32,598,21,494,14,647,25,646,644,645,639,638,26,637,636,643,24,642,640,641,28,659,658,656,657,29,651,650,649,648,27,655,654,653,652,702,701,703,704,193,422,155,159,584,194,153,160,582,420,192,421,154,161,583,196,151,425,158,587,197,152,423,156,585,195,150,424,157,586,146,199,428,165,590,166,144,200,426,588,145,198,427,167,589,202,149,431,164,593,203,147,429,162,591,201,148,430,163,592,698,697,694,700,6,458,268,536,374,7,269,534,372,456,8,457,267,535,373,9,264,461,539,377,10,265,459,537,375,11,266,460,538,376,274,4,464,542,380,540,275,5,462,378,273,3,463,541,379,1,270,467,545,383,0,271,465,543,381,2,272,466,544,382,681,674,677,684,211,434,512,470,626,212,510,468,624,432,210,433,511,469,625,214,515,437,473,629,215,513,435,471,627,213,514,436,472,628,518,209,440,476,632,474,516,207,438,630,517,208,439,475,631,205,521,443,479,635,206,519,441,477,633,204,520,442,478,634,678,683,676,680,257,353,362,137,614,255,360,135,612,351,256,352,361,136,613,253,365,349,133,617,254,363,350,134,615,252,364,348,132,616,368,263,359,143,620,141,366,261,357,618,367,262,358,142,619,259,371,355,139,623,260,369,356,140,621,258,370,354,138,622,688,692,690,685 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#dd5d8cb242321da00ce62fc2d476849be658b6b0a3d2fd229095425016dc303c, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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 21:12:54 · history