Equation 677 Database

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Magma 1d7b6fc71b36…

magma 1d7b6fc71b36
Size
705
Isomorphism class hash
1d7b6fc71b36e5b4352e755bc5fc9c8a6159dab6637f6e7465e49dab5f4b4bec
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 15:56:22
Display reorder
660,467,275,3,431,243,429,273,465,4,244,430,274,466,5,245,271,427,463,2,242,428,1,272,464,240,270,426,462,0,241,422,458,266,9,249,420,456,264,10,250,421,457,265,11,251,461,425,269,8,248,459,423,267,6,246,460,424,268,7,247,663,668,671,665,539,333,72,443,503,441,334,537,73,501,442,335,538,74,502,332,439,535,75,499,440,76,330,536,500,331,438,534,77,498,434,530,324,70,494,432,528,325,71,492,433,529,326,69,493,533,437,327,66,497,531,435,328,67,495,532,436,329,68,496,686,690,687,688,575,90,258,632,599,630,91,573,259,597,631,92,574,260,598,93,628,571,261,595,629,262,94,572,596,95,627,570,263,594,623,566,96,256,590,621,564,97,257,588,622,565,98,255,589,569,626,99,252,593,567,624,100,253,591,568,625,101,254,592,672,662,670,669,35,237,200,419,455,417,238,33,198,453,418,239,34,199,454,236,415,31,203,451,416,201,234,32,452,235,414,30,202,450,410,26,228,195,446,408,24,229,196,444,409,25,230,197,445,29,413,231,194,449,27,411,232,192,447,28,412,233,193,448,676,681,677,674,37,211,479,395,551,393,212,38,477,549,394,210,36,478,550,214,391,40,475,547,392,476,215,41,548,213,390,39,474,546,386,43,209,470,542,384,44,207,468,540,385,42,208,469,541,46,389,205,473,545,47,387,206,471,543,45,388,204,472,544,661,666,667,664,363,189,353,383,343,381,190,364,351,344,382,191,365,352,342,188,379,362,349,346,380,350,186,360,347,187,378,361,348,345,374,369,180,359,341,372,370,181,357,339,373,371,182,358,340,368,377,183,355,337,366,375,184,356,338,367,376,185,354,336,696,695,694,693,656,169,658,657,659,651,170,650,648,649,653,168,652,654,655,165,179,606,639,152,177,640,166,607,150,167,178,608,641,151,171,601,160,634,156,172,602,161,635,157,173,600,159,633,158,604,174,163,637,155,605,175,164,638,153,603,176,162,636,154,703,702,704,701,289,226,282,647,646,642,227,290,283,643,644,225,288,284,645,222,513,292,285,511,514,286,223,293,512,224,515,291,287,510,51,295,217,280,506,52,296,218,281,504,53,294,216,279,505,298,50,220,276,509,299,48,221,277,507,297,49,219,278,508,699,697,700,698,407,322,587,13,491,14,323,405,585,489,12,321,406,586,490,318,16,403,583,487,17,584,319,404,488,320,15,402,582,486,19,398,313,578,482,20,396,314,576,480,18,397,312,577,481,401,22,316,581,485,399,23,317,579,483,400,21,315,580,484,673,683,678,675,65,308,563,620,527,618,306,63,561,525,619,307,64,562,526,311,616,61,559,523,617,560,309,62,524,310,615,60,558,522,611,56,303,554,518,609,54,304,552,516,610,55,305,553,517,59,614,302,557,521,57,612,300,555,519,58,613,301,556,520,684,680,679,682,109,85,148,119,129,117,86,110,149,130,118,84,108,147,131,88,115,112,144,128,116,145,89,113,126,87,114,111,146,127,125,107,83,139,135,123,105,81,140,136,124,106,82,138,137,103,121,79,142,134,104,122,80,143,132,102,120,78,141,133,685,692,689,691 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#24d4369d63c88701266d916dc6f9c75e12853e26a0a22f3b011b6cf68ccd31bb, 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 15:56:24 · history