Equation 677 Database

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Magma 4655785cb9f0…

magma 4655785cb9f0
Size
705
Isomorphism class hash
4655785cb9f0952286c1f0a91cf1f402342d0682a1d8d783a8d77fe9de4027a8
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 16:45:06
Display reorder
660,179,90,119,97,66,67,91,177,117,98,68,92,178,118,96,69,182,93,115,100,180,70,94,116,101,181,71,95,114,99,185,88,64,110,103,89,65,108,183,104,87,63,109,184,102,60,84,113,188,106,85,61,111,186,107,62,86,112,187,105,669,665,663,662,58,506,482,148,593,591,504,59,480,149,592,505,57,481,147,589,54,502,478,151,55,590,503,479,152,56,588,501,477,150,49,512,599,488,146,510,597,486,50,144,511,598,487,48,145,595,508,484,52,142,509,596,485,53,143,594,507,483,51,141,688,686,687,691,203,605,470,617,434,432,603,201,468,615,433,604,202,469,616,430,206,601,466,613,204,431,602,467,614,205,429,600,465,612,209,611,440,476,623,609,438,474,207,621,610,439,475,208,622,436,607,472,212,619,608,437,473,210,620,435,606,471,211,618,670,666,672,664,31,297,458,314,530,528,298,33,456,312,529,299,34,457,313,526,28,300,454,310,25,527,301,455,311,26,525,302,453,309,23,303,536,464,320,304,534,462,21,318,305,535,463,22,319,532,306,460,19,316,307,533,461,20,317,531,308,459,18,315,681,677,680,679,323,277,494,289,386,384,278,321,492,290,385,276,322,493,288,382,326,273,490,285,324,383,274,491,286,325,381,275,489,287,329,283,392,500,295,284,390,498,327,296,282,391,499,328,294,388,279,496,332,291,280,389,497,330,292,387,281,495,331,293,668,667,671,661,194,446,629,82,46,47,444,192,627,83,45,445,193,628,81,42,190,442,625,78,191,43,443,626,79,189,44,441,624,80,200,452,37,635,73,450,38,633,198,74,451,36,634,199,72,40,448,631,196,76,449,41,632,197,77,39,447,630,195,75,697,700,696,693,6,562,542,127,584,582,563,7,540,128,583,561,8,541,126,580,9,558,538,123,10,581,559,539,124,11,579,560,537,125,4,658,659,656,657,651,650,648,5,649,654,655,652,3,653,586,564,544,1,121,565,587,545,0,122,585,566,543,2,120,701,702,703,704,336,551,572,398,422,420,549,337,570,396,421,550,338,571,397,418,335,547,568,394,333,419,548,569,395,334,417,546,567,393,342,557,428,578,404,555,426,576,343,402,556,427,577,344,403,424,553,574,341,400,554,425,575,339,401,423,552,573,340,399,694,699,698,695,264,518,410,166,131,129,516,265,408,167,130,517,266,409,165,134,263,514,406,169,261,132,515,407,170,262,133,513,405,168,270,524,137,416,172,522,135,414,271,173,523,136,415,272,171,140,520,412,269,175,521,138,413,267,176,139,519,411,268,174,676,675,678,684,32,353,641,361,374,372,351,35,639,362,373,352,30,640,360,370,24,356,637,357,27,371,354,638,358,29,369,355,636,359,16,348,380,647,367,349,378,645,17,368,350,379,646,15,366,376,347,643,12,363,345,377,644,13,364,375,346,642,14,365,673,683,682,674,157,240,222,250,225,226,241,158,223,251,227,242,156,224,249,228,153,239,221,253,154,229,237,219,254,155,230,238,220,252,163,246,231,213,256,247,232,214,164,257,248,233,215,162,255,234,245,216,159,259,243,235,217,160,260,236,244,218,161,258,692,685,689,690 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#3d4915088e45e024e7bce9a29cd7ec921add83e4b04ab0fb3d527eb1a5f02fc2, 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 16:45:10 · history