Equation 677 Database

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Magma 3fc074a723a5…

magma 3fc074a723a5
Size
705
Isomorphism class hash
3fc074a723a59ad48d97144d3e44da29e782aa035dfae01fffd9ab50f3a17b9a
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 19:07:29
Display reorder
704,539,99,519,563,520,537,561,100,521,101,538,562,98,518,535,559,96,516,536,560,97,517,534,558,525,105,554,530,526,106,552,528,527,107,553,529,104,524,557,533,102,522,555,531,103,523,556,532,544,545,543,540,541,542,550,551,548,546,547,549,663,661,660,662,347,79,327,371,328,345,369,80,329,78,346,370,82,326,343,367,83,324,344,368,81,325,342,366,333,77,362,338,334,75,360,336,335,76,361,337,73,332,365,341,74,330,363,339,72,331,364,340,352,353,351,348,349,350,358,359,356,354,355,357,689,690,691,688,611,27,591,580,592,609,581,28,593,29,610,579,26,590,607,576,24,588,608,577,25,589,606,578,597,33,586,602,598,34,587,600,599,35,585,601,32,596,582,605,30,594,583,603,31,595,584,604,569,567,568,565,566,564,575,573,570,571,572,574,669,670,671,668,389,168,376,418,377,387,419,169,375,170,388,417,171,372,385,414,172,373,386,415,173,374,384,416,382,174,409,395,383,175,410,393,381,176,408,394,177,378,412,391,178,379,413,392,179,380,411,390,402,403,404,405,406,407,400,401,398,396,397,399,677,679,678,676,191,17,226,212,227,189,210,15,225,16,190,211,13,222,187,215,14,223,188,213,12,224,186,214,217,23,207,182,218,21,208,180,216,22,209,181,19,220,206,185,20,221,204,183,18,219,205,184,195,196,197,194,192,193,201,202,199,200,198,203,665,667,666,664,656,659,658,657,650,648,649,651,654,655,652,653,643,642,640,641,647,646,644,645,639,638,636,637,622,623,621,620,614,615,613,612,618,619,617,616,635,634,632,633,627,626,625,624,631,630,628,629,93,94,95,92,90,91,84,85,89,87,88,86,694,693,692,695,159,117,155,135,153,160,136,118,154,119,161,137,116,151,158,134,114,152,156,132,115,150,157,133,146,108,141,165,144,109,142,166,145,110,143,167,111,149,140,164,112,147,138,162,113,148,139,163,129,130,131,128,126,127,120,121,125,123,124,122,702,701,700,703,261,59,243,230,244,262,228,57,245,58,263,229,55,242,260,233,56,240,258,231,54,241,259,232,249,50,236,252,250,48,234,253,251,49,235,254,53,248,239,255,51,246,237,256,52,247,238,257,275,273,274,271,272,270,266,264,268,269,267,265,698,697,696,699,499,42,481,468,482,500,469,43,480,44,498,470,45,484,502,471,46,485,503,472,47,483,501,473,487,40,474,497,488,41,475,495,486,39,476,496,36,490,477,493,37,491,478,494,38,489,479,492,505,506,504,508,509,507,511,512,513,514,515,510,673,674,675,672,297,68,284,314,282,298,312,66,283,67,299,313,71,287,296,317,69,285,294,315,70,286,295,316,279,63,320,288,280,64,318,289,281,65,319,290,62,278,323,291,60,276,321,292,61,277,322,293,311,309,310,307,308,306,302,300,304,305,303,301,683,682,680,681,465,2,453,441,454,466,442,1,455,0,467,443,5,452,464,440,3,450,462,438,4,451,463,439,444,8,432,456,445,6,433,457,446,7,434,458,11,447,435,459,9,448,436,460,10,449,437,461,430,431,429,426,427,428,421,422,423,424,425,420,687,685,684,686 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#8782a898cb34e59b9ea1a81d727d55f661339e265a029f2d4530f64cefd9daa9, 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 19:07:30 · history