Equation 677 Database

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Magma 948f4f4c48ea…

magma 948f4f4c48ea
Size
705
Isomorphism class hash
948f4f4c48ea7f3b36d19af7e5f9821fd30db6c4a527152c44661f318dc9cdce
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 15:24:45
Display reorder
704,13,12,14,15,16,17,18,4,5,6,7,8,9,10,11,21,22,23,24,25,26,27,28,29,30,31,32,33,19,20,45,46,47,48,34,35,36,37,38,39,40,41,42,43,59,60,61,62,63,49,50,51,52,53,54,55,56,57,58,44,661,663,662,660,211,210,212,213,199,200,201,202,203,204,205,206,207,208,209,188,189,190,191,192,193,194,195,196,197,198,184,185,186,187,231,232,233,234,235,236,237,238,239,240,241,242,243,229,223,224,225,226,227,228,214,215,216,217,218,219,220,221,222,230,691,690,688,689,526,525,527,528,514,515,516,517,518,519,520,521,522,523,524,543,529,530,531,532,533,534,535,536,537,538,539,540,541,542,511,512,513,499,500,501,502,503,504,505,506,507,508,509,488,489,490,491,492,493,494,495,496,497,498,484,485,486,487,510,668,669,670,671,273,272,259,260,261,262,263,264,265,266,267,268,269,270,271,256,257,258,244,245,246,247,248,249,250,251,252,253,254,255,290,291,292,293,294,295,296,297,298,299,300,301,302,303,279,280,281,282,283,284,285,286,287,288,274,275,276,277,278,289,677,676,678,679,352,351,353,354,355,356,357,358,359,360,361,362,363,349,350,347,348,334,335,336,337,338,339,340,341,342,343,344,345,346,318,304,305,306,307,308,309,310,311,312,313,314,315,316,326,327,328,329,330,331,332,333,319,320,321,322,323,324,325,317,667,666,665,664,657,659,656,658,634,635,636,637,638,639,0,2,3,1,655,645,646,647,648,649,650,651,652,653,654,640,641,642,643,644,631,632,633,619,620,621,622,623,624,625,626,627,628,629,608,609,610,611,612,613,614,615,616,617,618,604,605,606,607,630,695,692,694,693,560,559,561,562,563,564,565,566,567,568,569,570,571,572,573,549,550,551,552,553,554,555,556,557,558,544,545,546,547,548,589,590,591,592,593,594,595,596,597,598,599,600,601,602,575,576,577,578,579,580,581,582,583,584,585,586,587,588,574,603,702,700,701,703,376,375,377,378,364,365,366,367,368,369,370,371,372,373,374,393,379,380,381,382,383,384,385,386,387,388,389,390,391,392,396,397,398,399,400,401,402,403,404,405,406,407,408,394,413,414,415,416,417,418,419,420,421,422,423,409,410,411,412,395,697,698,699,696,183,182,169,170,171,172,173,174,175,176,177,178,179,180,181,166,167,168,154,155,156,157,158,159,160,161,162,163,164,165,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,124,672,673,674,675,448,447,449,450,451,452,453,439,440,441,442,443,444,445,446,431,432,433,434,435,436,437,438,424,425,426,427,428,429,430,480,481,482,483,469,470,471,472,473,474,475,476,477,478,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,479,682,683,681,680,108,107,94,95,96,97,98,99,100,101,102,103,104,105,106,116,117,118,119,120,121,122,123,109,110,111,112,113,114,115,90,91,92,93,79,80,81,82,83,84,85,86,87,88,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,89,684,685,686,687 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#17d8eb76b6bf5b6d0c7c94cbffab8bf30c3f61585a1079f6e7ebccc76f8bf7d1, 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 15:24:48 · history