Equation 677 Database

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Magma 9f20c5fcfa29…

magma 9f20c5fcfa29
Size
705
Isomorphism class hash
9f20c5fcfa29cb19cd61aa98240597024d6fccb94447c47843d59f53241640cd
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 17:37:28
Display reorder
660,89,531,182,447,377,87,532,180,448,375,533,449,88,181,376,92,530,185,446,373,528,90,183,444,374,91,529,184,445,372,177,84,522,438,368,178,85,523,439,366,179,86,524,440,367,83,176,525,441,371,81,174,526,442,369,82,175,527,443,370,665,662,671,670,168,287,275,263,257,169,285,273,261,255,286,262,170,274,256,171,283,271,259,253,284,172,272,260,254,173,282,270,258,252,281,166,293,269,248,279,167,291,267,246,280,165,292,268,247,162,277,289,265,251,163,278,290,266,249,164,276,288,264,250,685,686,690,689,205,483,589,411,399,206,484,590,412,400,485,413,204,591,401,208,482,588,410,398,480,209,586,408,396,207,481,587,409,397,580,203,474,402,390,581,201,475,403,391,582,202,476,404,392,199,583,477,405,393,200,584,478,406,394,198,585,479,407,395,663,661,667,672,296,228,519,102,133,294,229,520,100,134,230,101,295,521,132,299,231,518,105,136,232,297,516,103,137,298,233,517,104,135,510,302,226,108,131,511,300,227,106,129,512,301,225,107,130,305,513,222,111,127,303,514,223,109,128,304,515,224,110,126,676,680,675,677,5,507,495,236,435,3,508,496,234,436,509,235,4,497,437,0,506,494,239,434,504,2,492,237,432,1,505,493,238,433,486,11,498,242,426,487,9,499,240,427,488,10,500,241,428,7,489,501,245,429,8,490,502,243,430,6,491,503,244,431,666,664,669,668,469,623,543,379,622,470,625,544,380,624,627,378,468,545,626,472,621,542,382,620,617,473,540,383,616,471,619,541,381,618,534,467,604,385,605,535,465,606,386,607,536,466,609,384,608,463,537,611,388,610,464,538,612,389,613,462,539,614,387,615,693,698,697,694,219,118,579,122,93,220,654,655,652,653,656,657,221,659,658,218,119,578,26,123,120,216,576,24,124,217,121,577,25,125,570,210,116,29,96,571,211,117,27,94,572,212,115,28,95,213,573,112,32,99,214,574,113,30,97,215,575,114,31,98,702,703,701,704,50,555,44,646,647,48,556,42,649,648,557,651,49,43,650,46,554,40,645,644,552,47,41,640,641,45,553,39,643,642,35,56,546,628,629,33,54,547,631,630,34,55,548,633,632,52,38,549,634,635,53,36,550,636,637,51,37,551,639,638,699,700,695,696,453,22,364,601,423,454,23,365,602,424,21,603,455,363,425,452,18,360,600,422,19,450,361,598,420,451,20,362,599,421,355,459,13,592,414,356,460,14,593,415,354,461,12,594,416,458,358,16,595,417,456,359,17,596,418,457,357,15,597,419,681,674,673,682,161,73,62,196,567,159,74,60,197,568,72,195,160,61,569,157,69,58,192,566,70,158,59,193,564,156,71,57,194,565,68,152,79,187,558,66,150,80,188,559,67,151,78,186,560,155,64,75,190,561,153,65,76,191,562,154,63,77,189,563,684,679,678,683,147,335,329,314,346,148,333,327,312,347,334,313,149,328,345,146,331,325,317,342,332,144,326,315,343,145,330,324,316,344,320,138,341,309,352,318,139,339,310,353,319,140,340,311,351,141,323,337,308,348,142,321,338,306,349,143,322,336,307,350,687,688,692,691 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#5aa74a2d4b4bbe4036558963ef968fca94fa5f577bdbfbf2823cea2791e8d20b, 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 17:37:29 · history