Equation 677 Database

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Magma 917d0302c2e4…

magma 917d0302c2e4
Size
705
Isomorphism class hash
917d0302c2e45ca3f56f924b64a3cf1fbf00195e75cd018421aab0bfd17a4b82
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 20:44:18
Display reorder
660,560,572,578,3,575,4,592,581,598,595,5,552,540,558,555,632,2,620,638,635,652,1,641,658,655,612,0,600,618,615,9,521,538,532,535,10,481,498,492,495,11,501,518,512,515,440,8,449,445,446,461,6,476,470,473,420,7,436,430,433,693,697,699,690,570,576,573,229,564,230,596,590,593,584,228,556,550,553,544,636,232,630,633,624,656,233,650,653,644,616,231,610,613,604,235,530,533,536,524,236,490,493,496,484,234,510,513,516,504,454,238,455,447,442,469,239,471,474,463,429,237,431,434,423,702,688,689,696,367,119,355,135,71,136,117,368,356,69,137,118,366,354,70,115,134,370,358,67,116,132,371,359,68,114,133,369,357,66,141,365,353,110,62,142,363,351,108,60,143,364,352,109,61,361,140,349,113,65,362,138,350,111,63,360,139,348,112,64,661,672,671,673,16,415,343,187,164,188,416,17,344,162,186,414,15,342,163,418,190,12,346,167,419,191,13,347,165,417,189,14,345,166,185,22,341,413,159,183,23,339,411,160,184,21,340,412,161,18,181,337,409,158,19,182,338,410,156,20,180,336,408,157,664,666,669,681,565,566,569,127,563,128,586,585,589,583,126,546,545,549,543,626,130,625,629,623,646,131,645,649,643,606,129,605,609,603,125,525,529,526,523,123,485,489,486,483,124,505,509,506,503,443,121,444,451,450,464,122,468,465,462,424,120,428,425,422,704,700,685,694,579,567,574,169,568,170,587,599,594,588,168,547,559,554,548,627,172,639,634,628,647,173,659,654,648,607,171,619,614,608,175,539,534,527,528,176,499,494,487,488,174,519,514,507,508,457,178,456,452,453,477,179,472,466,467,437,177,432,426,427,695,701,692,703,561,577,571,39,562,40,597,580,591,582,41,557,541,551,542,637,38,621,631,622,657,36,640,651,642,617,37,601,611,602,45,520,531,537,522,46,480,491,497,482,47,500,511,517,502,459,44,458,448,441,479,42,478,475,460,439,43,438,435,421,687,686,691,698,256,267,286,219,403,220,268,257,287,404,221,269,255,285,402,266,218,252,282,406,264,216,253,283,407,265,217,254,284,405,225,262,277,273,401,226,263,278,274,399,227,261,276,275,400,258,224,280,272,397,259,222,281,270,398,260,223,279,271,396,680,676,682,662,307,319,154,196,56,197,320,308,155,54,195,318,306,153,55,322,192,310,150,59,323,193,311,151,57,321,194,309,152,58,202,305,145,317,51,203,303,146,315,52,201,304,144,316,53,301,198,148,313,50,302,199,149,314,48,300,200,147,312,49,684,665,678,667,97,80,391,241,331,242,78,98,392,332,240,79,96,390,330,83,244,100,394,334,81,245,101,395,335,82,243,99,393,333,247,103,389,75,329,248,104,387,76,327,246,102,388,77,328,106,250,385,74,325,107,251,386,72,326,105,249,384,73,324,668,683,675,679,379,291,211,31,94,32,292,380,212,95,30,293,378,210,93,290,34,382,214,90,288,35,383,215,91,289,33,381,213,92,29,377,209,297,85,27,375,207,298,86,28,376,208,299,84,373,25,205,296,88,374,26,206,294,89,372,24,204,295,87,670,674,677,663 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#d283ee665ba0250146cee526d5335dad060ba0eb857bd84eda99570515d555dc, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 20:44:19 · history