Equation 677 Database

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Magma 45b5434b8b1a…

magma 45b5434b8b1a
Size
705
Isomorphism class hash
45b5434b8b1a6fe7dba2946ecd75cfb0fd001f63c3e2bbaf5ca8c1cebd05cecf
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 15:52:07
Display reorder
660,483,485,484,481,482,480,491,489,490,487,488,486,428,426,427,431,429,430,423,424,425,422,420,421,607,608,606,610,611,609,605,603,604,601,602,600,548,546,547,551,549,550,543,544,545,542,540,541,5,3,4,0,2,1,11,9,10,7,8,6,663,671,665,673,275,274,273,270,271,272,265,266,264,268,269,267,390,391,392,393,394,395,388,389,387,384,385,386,190,191,189,186,187,188,181,182,180,184,185,183,333,334,335,332,330,331,324,325,326,327,328,329,110,108,109,113,111,112,116,114,115,119,117,118,682,689,690,694,454,453,455,452,450,451,444,445,446,447,448,449,564,565,566,567,568,569,570,571,572,573,574,575,167,165,166,163,164,162,158,156,157,161,159,160,627,628,629,626,624,625,633,634,635,632,630,631,514,515,513,510,511,512,505,506,504,508,509,507,662,664,670,675,194,193,192,196,197,195,199,200,198,202,203,201,286,287,285,282,283,284,277,278,276,280,281,279,175,176,174,178,179,177,173,171,172,169,170,168,345,346,347,344,342,343,336,337,338,339,340,341,128,126,127,131,129,130,123,124,125,122,120,121,667,678,680,685,151,150,152,153,154,155,148,149,147,144,145,146,48,49,50,51,52,53,54,55,56,57,58,59,293,291,292,289,290,288,299,297,298,295,296,294,140,138,139,143,141,142,135,136,137,134,132,133,352,353,351,348,349,350,358,359,357,354,355,356,661,672,666,674,493,492,494,495,496,497,498,499,500,501,502,503,612,613,614,615,616,617,618,619,620,621,622,623,66,67,68,69,70,71,64,65,63,60,61,62,434,432,433,437,435,436,440,438,439,443,441,442,554,552,553,557,555,556,560,558,559,563,561,562,691,695,696,700,103,102,104,105,106,107,100,101,99,96,97,98,403,404,402,406,407,405,401,399,400,397,398,396,92,90,91,95,93,94,87,88,89,86,84,85,414,415,416,417,418,419,412,413,411,408,409,410,83,81,82,79,80,78,74,72,73,77,75,76,699,702,704,703,47,46,45,42,43,44,37,38,36,40,41,39,300,301,302,303,304,305,306,307,308,309,310,311,217,218,216,220,221,219,223,224,222,226,227,225,247,248,246,250,251,249,245,243,244,241,242,240,369,370,371,368,366,367,360,361,362,363,364,365,692,697,698,701,589,588,590,591,592,593,594,595,596,597,598,599,528,529,530,531,532,533,534,535,536,537,538,539,20,18,19,23,21,22,15,16,17,14,12,13,474,475,476,477,478,479,472,473,471,468,469,470,656,654,655,659,657,658,651,652,653,650,648,649,669,677,676,684,228,230,229,233,231,232,236,234,235,239,237,238,206,204,205,209,207,208,212,210,211,215,213,214,319,320,318,322,323,321,317,315,316,313,314,312,383,381,382,379,380,378,374,372,373,377,375,376,259,260,258,262,263,261,257,255,256,253,254,252,668,679,681,686,580,579,581,578,576,577,585,586,587,584,582,583,637,638,636,640,641,639,643,644,642,646,647,645,26,24,25,29,27,28,32,30,31,35,33,34,521,519,520,517,518,516,527,525,526,523,524,522,464,462,463,467,465,466,459,460,461,458,456,457,683,688,687,693 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#22cb8afe1ff0462b448663f4450c6ce0a1106142be9f7b23381e657feeb5c2cf, M = {62} 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 15:52:09 · history