Equation 677 Database

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Magma cbf7d65dfa2d…

magma cbf7d65dfa2d
Size
705
Isomorphism class hash
cbf7d65dfa2de5433b658d14231703bc3bc668b705605aa993518b3e6737303c
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 19:54:46
Display reorder
660,435,52,387,187,175,436,54,173,388,185,437,50,174,389,186,46,434,171,386,183,47,432,172,384,184,49,433,170,385,182,41,441,166,393,178,42,442,164,394,176,40,443,165,395,177,440,44,169,392,181,390,438,45,167,179,439,43,168,391,180,664,668,662,661,34,256,447,571,599,35,257,600,448,572,36,258,601,449,573,259,37,598,446,570,260,38,596,444,568,261,39,597,445,569,262,32,605,453,577,263,33,606,454,578,264,31,607,455,579,28,265,604,452,576,450,29,266,602,574,30,267,603,451,575,685,689,688,686,583,112,555,162,142,584,110,140,556,163,585,111,141,557,161,115,582,145,554,158,113,580,143,552,159,114,581,144,553,160,107,589,148,561,153,108,590,146,562,154,109,591,147,563,152,588,106,151,560,156,558,586,104,149,157,587,105,150,559,155,671,667,665,669,315,56,278,303,285,313,57,283,279,301,314,58,284,277,302,59,311,281,274,299,60,312,282,275,300,61,310,280,276,298,62,306,291,269,294,63,304,289,270,292,64,305,290,268,293,309,65,287,272,297,273,307,66,288,295,308,67,286,271,296,673,682,676,683,495,225,423,331,317,496,226,318,424,332,497,224,316,425,333,228,494,320,422,330,229,492,321,420,328,227,493,319,421,329,231,501,323,429,337,232,502,324,430,338,230,503,322,431,339,500,234,326,428,336,426,498,235,327,334,499,233,325,427,335,666,672,670,663,459,189,507,531,411,460,190,412,508,532,461,188,413,509,533,192,458,410,506,530,193,456,408,504,528,191,457,409,505,529,195,465,417,513,537,196,466,418,514,538,194,467,419,515,539,464,198,416,512,536,510,462,199,414,534,463,197,415,511,535,695,694,698,696,567,14,595,3,48,631,15,630,628,629,633,13,632,634,635,10,566,55,592,2,11,564,51,593,1,12,565,53,594,0,5,649,648,650,651,6,653,652,654,655,4,657,656,658,659,644,8,645,646,647,638,636,9,637,639,640,7,641,642,643,701,702,704,703,347,217,68,238,22,345,215,23,69,239,346,216,24,70,240,213,343,25,71,241,214,344,26,72,242,212,342,27,73,243,223,623,20,74,622,221,624,21,75,625,222,626,19,76,627,620,219,16,77,621,78,341,220,17,236,340,218,18,79,237,699,693,700,697,471,377,543,611,519,472,375,520,544,612,473,376,521,545,613,373,470,518,542,610,374,468,516,540,608,372,469,517,541,609,383,477,525,549,617,381,478,526,550,618,382,479,527,551,619,476,379,524,548,616,546,474,380,522,614,475,378,523,547,615,677,680,684,681,363,244,483,356,399,364,245,400,484,354,365,246,401,485,355,247,362,398,482,359,248,360,396,480,357,249,361,397,481,358,250,369,405,489,351,251,370,406,490,352,252,371,407,491,353,368,253,404,488,350,486,366,254,402,348,367,255,403,487,349,674,675,679,678,129,95,81,125,206,130,96,207,82,126,128,97,208,80,127,94,132,209,84,124,92,133,210,85,122,93,131,211,83,123,101,135,204,87,116,102,136,205,88,117,103,134,203,86,118,138,100,200,90,119,91,139,98,201,120,137,99,202,89,121,690,691,687,692 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#b356224f433e80b1c4ac338e7aaea2066ee34f4a7233e2d09dbcc6e7070accf0, 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 19:54:47 · history