Equation 677 Database

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Magma 6c3010c85ce1…

magma 6c3010c85ce1
Size
705
Isomorphism class hash
6c3010c85ce17f075683c5334c81a20c9cc7eedb727fe713da2af05b65f867a9
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 16:26:37
Display reorder
660,261,265,539,62,285,259,266,537,63,283,260,267,538,61,284,264,257,535,65,281,262,258,536,66,282,256,263,534,64,280,252,68,271,545,276,250,69,272,543,274,251,67,273,544,275,71,255,270,541,279,72,253,268,542,277,70,254,269,540,278,667,666,672,661,468,79,496,141,85,466,80,492,139,86,467,81,494,140,87,82,464,488,144,88,83,465,491,142,89,463,84,487,143,90,474,136,77,508,91,472,137,78,505,92,473,138,76,507,93,135,470,73,501,94,133,471,74,502,95,134,469,75,499,96,689,687,691,686,515,40,225,303,563,513,41,223,301,561,514,42,224,302,562,39,511,221,299,559,37,512,222,300,560,510,38,220,298,558,521,309,46,216,569,519,307,47,214,567,520,308,48,215,568,305,517,45,219,565,306,518,43,217,566,304,516,44,218,564,668,670,669,665,441,447,152,208,19,439,445,153,209,20,440,446,151,210,21,443,437,155,211,22,444,438,156,212,23,436,442,154,213,24,432,206,453,150,17,430,207,451,148,18,431,205,452,149,16,202,435,449,146,13,203,433,450,147,14,204,434,448,145,15,681,673,678,682,180,423,164,30,629,178,421,165,28,627,179,422,163,29,628,419,176,167,26,625,420,177,168,27,626,175,418,166,25,624,171,36,429,162,635,169,34,427,160,633,170,35,428,161,634,32,174,425,158,631,33,172,426,159,632,31,173,424,157,630,671,662,663,664,399,339,527,287,98,397,337,525,288,99,398,338,526,286,97,335,395,523,290,101,336,396,524,291,102,394,334,522,289,100,405,293,345,533,104,403,294,343,531,105,404,292,344,532,103,296,401,341,529,107,297,402,342,530,108,295,400,340,528,106,693,697,695,696,595,184,575,199,459,596,185,573,200,457,594,186,574,201,458,183,591,571,198,455,181,592,572,196,456,593,182,570,197,454,659,190,657,658,656,651,191,649,650,648,655,192,653,654,652,193,597,189,577,461,194,598,187,578,462,195,599,188,576,460,702,703,701,704,347,118,584,362,605,348,119,582,363,603,346,120,583,361,604,117,350,580,358,601,115,351,581,359,602,349,116,579,360,600,353,368,109,590,611,354,369,110,588,609,352,367,111,589,610,364,356,112,586,607,365,357,113,587,608,366,355,114,585,606,700,698,699,694,12,551,327,244,480,10,549,325,245,478,11,550,326,246,479,547,8,323,247,476,548,9,324,248,477,7,546,322,249,475,3,242,557,333,486,0,243,555,331,484,2,241,556,332,485,238,6,553,329,482,239,4,554,330,483,240,5,552,328,481,679,674,680,684,411,379,641,122,387,409,380,639,123,385,410,381,640,121,386,378,407,637,125,383,376,408,638,126,384,406,377,636,124,382,417,128,370,647,393,415,129,371,645,391,416,127,372,646,392,131,413,373,643,389,132,414,374,644,390,130,412,375,642,388,676,683,675,677,617,49,497,315,233,615,50,493,313,234,616,51,495,314,232,52,613,489,311,236,53,614,490,312,237,612,54,1,310,235,623,321,55,509,231,621,319,56,504,229,622,320,57,506,230,317,619,58,500,227,318,620,59,503,228,316,618,60,498,226,690,688,685,692 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#31b39e995794136cb14e9cfb9c49dab141b331fe9ae7acf51f9a6bc9a2946638, 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 16:26:38 · history