Equation 677 Database

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Magma 64df7bb1e554…

magma 64df7bb1e554
Size
705
Isomorphism class hash
64df7bb1e554feddd84176f58247e632ecf4530a7da4da83eb4d40452f961356
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 19:13:23
Display reorder
660,334,394,90,299,323,300,335,395,91,324,396,298,336,92,322,295,333,393,93,319,296,331,391,94,320,297,332,392,95,321,340,400,88,305,329,341,401,89,306,330,342,402,87,304,328,339,399,84,301,325,337,397,85,302,326,338,398,86,303,327,661,672,662,666,406,60,55,150,454,151,407,61,56,455,62,152,408,54,456,153,405,63,58,453,154,403,64,59,451,155,404,65,57,452,412,66,53,148,460,413,67,51,149,461,414,68,52,147,462,411,69,49,144,459,409,70,50,145,457,410,71,48,146,458,685,686,688,687,256,227,268,111,240,112,257,228,269,238,226,113,258,270,239,110,255,223,267,236,108,253,224,265,237,109,254,225,266,235,247,233,259,117,246,248,234,260,118,244,249,232,261,119,245,250,229,262,116,242,251,230,263,114,243,252,231,264,115,241,670,667,669,668,162,382,20,80,358,78,163,383,21,359,384,79,164,22,360,83,165,381,19,357,81,166,379,17,355,82,167,380,18,356,160,388,11,75,364,161,389,12,76,365,159,390,13,77,366,156,387,14,74,363,157,385,15,72,361,158,386,16,73,362,676,674,682,673,442,489,631,170,535,168,443,490,632,536,491,169,444,633,537,173,441,488,630,534,171,439,486,628,532,172,440,487,629,533,448,495,637,176,541,449,496,638,174,542,450,497,639,175,543,447,494,636,179,540,445,492,634,177,538,446,493,635,178,539,664,665,663,671,346,31,222,100,418,101,347,32,220,419,30,99,348,221,420,96,345,34,218,417,97,343,35,219,415,98,344,33,217,416,352,29,213,106,424,353,27,211,107,425,354,28,212,105,426,351,25,216,102,423,349,26,214,103,421,350,24,215,104,422,693,695,694,698,475,201,525,8,196,9,476,202,526,197,203,10,477,527,195,7,478,204,524,199,5,479,205,522,200,6,480,206,523,198,481,207,531,0,485,655,653,654,1,652,656,658,659,23,657,482,210,530,2,193,483,208,528,3,194,484,209,529,4,192,703,702,701,704,466,607,513,183,583,184,467,608,514,584,609,185,468,515,585,182,465,606,512,582,180,463,604,510,580,181,464,605,511,581,472,613,519,189,589,473,614,520,190,590,474,615,521,191,591,471,612,518,188,588,469,610,516,186,586,470,611,517,187,587,700,699,696,697,501,559,293,311,136,312,502,560,294,137,561,310,503,292,135,307,500,558,289,132,308,498,556,290,133,309,499,557,291,134,507,565,284,317,142,508,566,285,318,143,509,567,283,316,141,506,564,287,313,138,504,562,288,314,139,505,563,286,315,140,681,677,679,684,547,370,430,47,643,45,548,371,431,644,372,46,549,432,645,43,546,369,429,642,44,544,367,427,640,42,545,368,428,641,553,376,436,38,649,554,377,437,36,650,555,378,438,37,651,552,375,435,41,648,550,373,433,39,646,551,374,434,40,647,675,683,680,678,619,595,281,122,571,120,620,596,282,572,597,121,621,280,573,125,618,594,277,570,123,616,592,278,568,124,617,593,279,569,625,601,272,128,577,626,602,273,126,578,627,603,271,127,579,624,600,275,131,576,622,598,276,129,574,623,599,274,130,575,691,689,692,690 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#90fd68087a2f09648803d65723dcc8788b62f036d4e0ed1478893fb37d6a20cd, 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 19:13:24 · history