Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 94f7beda3513…

magma 94f7beda3513
Size
705
Isomorphism class hash
94f7beda3513952f536e7f46ee1ba21377a59c05879980d0e62df357ad19be9a
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 19:50:15
Display reorder
660,513,516,515,27,508,535,533,28,528,536,495,496,493,29,488,436,435,433,26,429,453,452,450,24,448,476,475,473,25,468,636,635,33,633,628,656,655,34,653,648,616,615,35,613,608,557,558,32,555,550,577,578,30,575,570,597,598,31,595,590,685,699,689,703,507,500,506,253,511,526,527,254,531,520,486,481,487,252,491,422,427,428,256,431,454,458,459,257,446,461,466,467,255,471,620,626,259,627,631,641,646,260,647,651,600,606,258,607,611,546,540,262,547,553,566,561,263,567,573,586,581,261,587,593,688,694,695,691,404,328,376,268,81,377,406,269,82,329,375,327,402,267,83,324,372,396,264,80,325,373,398,265,78,326,374,401,266,79,334,382,274,417,72,335,383,275,418,73,333,381,273,415,74,378,330,270,409,75,379,331,271,411,76,380,332,272,412,77,682,674,668,666,115,405,388,51,133,389,116,52,134,407,387,403,114,53,132,397,384,118,50,136,399,385,119,48,137,400,386,117,49,135,416,394,57,113,139,419,395,58,111,140,414,393,59,112,138,390,408,56,109,142,391,410,54,110,143,392,413,55,108,141,665,678,672,681,512,501,510,159,502,530,532,160,522,521,490,480,492,161,482,420,430,432,158,423,443,445,447,156,444,460,470,472,157,462,621,630,165,632,622,640,650,166,652,642,601,610,167,612,602,552,541,164,554,542,572,560,162,574,562,592,580,163,594,582,697,693,704,701,518,519,517,122,509,537,538,120,529,539,497,499,498,121,489,439,437,438,125,421,442,440,441,123,449,479,478,477,124,469,639,638,128,637,629,657,658,126,659,649,619,618,127,617,609,548,559,131,549,551,568,579,129,569,571,588,599,130,589,591,690,702,692,696,505,504,503,192,514,523,525,193,534,524,483,484,485,194,494,425,424,426,195,434,456,455,457,196,451,464,463,465,197,474,624,623,198,625,634,644,643,199,645,654,604,603,200,605,614,543,544,201,545,556,563,564,202,565,576,583,584,203,585,596,698,686,687,700,66,103,93,145,18,94,67,146,19,104,95,102,68,144,20,106,92,69,148,21,107,90,70,149,22,105,91,71,147,23,101,84,151,64,16,99,85,152,65,17,100,86,150,63,15,87,97,154,60,12,88,98,155,61,13,89,96,153,62,14,684,663,670,677,364,286,292,39,316,293,365,40,317,287,291,285,363,41,315,282,288,360,38,312,283,289,361,36,313,284,290,362,37,314,277,298,45,370,322,278,299,46,371,323,276,297,47,369,321,294,280,44,366,318,295,281,42,367,319,296,279,43,368,320,673,662,664,679,240,340,226,301,233,227,241,302,231,341,225,339,242,300,232,336,222,243,304,229,337,223,244,305,230,338,224,245,303,228,346,217,307,246,239,347,218,308,247,237,345,216,306,248,238,220,342,310,249,235,221,343,311,250,236,219,344,309,251,234,676,680,683,667,8,352,169,211,180,170,6,212,181,353,168,351,7,210,182,348,172,11,214,183,349,173,9,215,184,350,171,10,213,185,358,175,209,3,186,359,176,207,4,187,357,174,208,5,188,178,354,205,2,189,179,355,206,1,190,177,356,204,0,191,661,671,675,669 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#b0c577ef9e4c05d7925e972279aa7c10376825c460b06aa55c85bf856c0bbca9, 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 19:50:16 · history