Equation 677 Database

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Magma 9e26c0e4f83b…

magma 9e26c0e4f83b
Size
705
Isomorphism class hash
9e26c0e4f83be9f94ae0215303054055f44878c8e68248069e893dfdaa1b2fca
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 21:18:38
Display reorder
660,596,10,253,170,359,594,11,168,254,357,169,9,595,252,358,13,592,173,256,355,14,593,171,257,356,12,591,172,255,354,587,16,259,176,350,585,17,260,174,348,586,15,258,175,349,590,19,262,179,353,588,20,263,177,351,589,18,261,178,352,668,663,671,670,62,512,572,319,232,60,510,320,570,233,318,511,61,571,231,508,65,322,568,228,509,63,323,569,229,507,64,321,567,230,57,503,563,317,238,58,501,561,315,239,59,502,562,316,237,56,506,566,313,234,54,504,564,314,235,55,505,565,312,236,688,690,685,689,443,476,560,278,116,441,474,276,558,114,277,475,442,559,115,472,439,281,556,119,473,440,279,557,117,471,438,280,555,118,434,467,551,284,122,432,465,549,282,120,433,466,550,283,121,437,470,554,287,125,435,468,552,285,123,436,469,553,286,124,667,664,666,669,76,584,79,324,159,77,582,325,80,160,326,583,75,78,161,580,72,327,82,158,581,73,328,83,156,579,74,329,81,157,67,575,85,330,165,68,573,86,331,166,66,574,84,332,167,70,578,88,333,164,71,576,89,334,162,69,577,87,335,163,681,673,677,676,391,347,407,96,608,392,345,97,405,606,98,346,390,406,607,343,394,99,403,604,344,395,100,404,605,342,393,101,402,603,389,338,398,94,599,387,336,396,95,597,388,337,397,93,598,385,341,401,90,602,386,339,399,91,600,384,340,400,92,601,662,672,661,665,500,26,536,187,270,498,24,188,534,271,186,25,499,535,272,22,496,190,532,273,23,497,191,533,274,21,495,189,531,275,491,32,527,185,268,489,30,525,183,269,490,31,526,184,267,494,28,530,181,264,492,29,528,182,265,493,27,529,180,266,693,698,695,697,659,658,656,145,657,651,650,146,649,648,144,654,655,653,652,450,640,148,39,2,451,641,149,40,1,452,639,147,41,0,635,445,37,151,5,633,446,38,152,3,634,444,36,150,4,638,448,33,154,8,636,449,34,155,6,637,447,35,153,7,701,703,704,702,647,464,524,214,646,642,462,215,522,643,213,463,644,523,645,460,200,210,520,202,461,198,211,521,203,459,199,212,519,201,141,455,515,205,196,142,453,513,206,197,143,454,514,204,195,140,458,518,208,192,138,456,516,209,193,139,457,517,207,194,694,699,700,696,488,307,51,251,431,486,308,249,52,429,250,306,487,53,430,310,484,247,50,427,311,485,248,48,428,309,483,246,49,426,479,305,42,242,422,477,303,43,240,420,478,304,44,241,421,482,301,45,245,425,480,302,46,243,423,481,300,47,244,424,682,675,678,684,548,106,419,219,632,546,107,220,417,630,221,105,547,418,631,102,544,218,415,628,103,545,216,416,629,104,543,217,414,627,539,112,410,225,623,537,113,408,226,621,538,111,409,227,622,542,108,413,224,626,540,109,411,222,624,541,110,412,223,625,679,683,680,674,620,383,367,137,297,618,381,135,368,298,136,382,619,366,299,379,616,133,370,296,380,617,134,371,294,378,615,132,369,295,611,374,365,128,288,609,372,363,126,289,610,373,364,127,290,614,377,361,131,291,612,375,362,129,292,613,376,360,130,293,686,691,692,687 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#e6bbf558fb3ffab686d395ed44cee4ecb6da0873fc29bc1527bdf36d2fd1603f, 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 21:18:39 · history