Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 8a9d0cc97639…

magma 8a9d0cc97639
Size
705
Isomorphism class hash
8a9d0cc97639e23e16d460e839b003c8386843a39b73cd69e7ceef2102ccda21
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 19:43:26
Display reorder
660,31,507,148,459,291,508,32,149,460,292,33,506,147,458,290,30,510,151,462,294,28,511,152,463,295,29,509,150,461,293,37,513,465,154,297,38,514,466,155,298,39,512,464,153,296,516,36,468,157,300,517,34,469,158,301,515,35,467,156,299,668,667,661,672,175,339,267,241,332,340,176,268,239,333,174,338,266,240,334,171,342,270,237,335,172,343,271,238,336,173,341,269,236,337,181,345,232,273,330,182,346,230,274,331,180,344,231,272,329,348,177,235,276,326,349,178,233,277,327,347,179,234,275,328,686,687,685,689,126,593,351,411,579,594,127,352,412,580,128,592,350,410,578,125,596,354,414,582,123,597,355,415,583,124,595,353,413,581,132,599,417,357,585,133,600,418,358,586,134,598,416,356,584,602,131,420,360,588,603,129,421,361,589,601,130,419,359,587,671,665,670,663,11,399,246,471,186,400,12,247,472,187,10,398,245,470,188,14,402,242,474,185,15,403,243,475,183,13,401,244,473,184,9,405,477,252,192,7,406,478,253,193,8,404,476,251,194,408,5,480,248,191,409,6,481,249,189,407,4,479,250,190,677,679,673,682,258,435,162,543,375,436,259,163,544,376,257,434,164,542,374,254,438,161,546,378,255,439,159,547,379,256,437,160,545,377,264,441,549,168,381,265,442,550,169,382,263,440,548,170,380,444,260,552,167,384,445,261,553,165,385,443,262,551,166,383,666,669,664,662,55,288,567,531,423,289,56,568,532,424,57,287,566,530,422,54,284,570,534,426,52,285,571,535,427,53,286,569,533,425,61,279,537,573,429,62,280,538,574,430,63,278,536,572,428,282,60,540,576,432,283,58,541,577,433,281,59,539,575,431,693,697,694,698,141,0,605,2,591,622,142,623,621,620,143,1,604,3,590,144,629,631,630,628,145,633,635,634,632,146,624,627,626,625,139,640,642,643,641,140,644,646,647,645,138,636,638,639,637,652,135,654,655,653,656,136,658,659,657,648,137,650,651,649,703,704,701,702,312,106,116,495,200,104,313,114,496,201,311,105,115,494,202,308,102,112,498,203,309,103,113,499,204,310,101,111,497,205,303,109,501,122,198,304,110,502,120,199,302,108,500,121,197,100,306,504,118,195,619,307,505,119,618,107,305,503,117,196,700,695,699,696,90,363,41,607,519,364,88,42,608,520,89,362,40,606,518,93,366,44,610,522,91,367,45,611,523,92,365,43,609,521,96,369,613,47,525,94,370,614,48,526,95,368,612,46,524,372,99,616,50,528,373,97,617,51,529,371,98,615,49,527,675,684,681,683,71,315,387,227,447,316,72,388,228,448,70,314,386,229,446,74,318,390,226,450,75,319,391,224,451,73,317,389,225,449,69,321,218,393,453,67,322,219,394,454,68,320,220,392,452,324,65,221,396,456,325,66,222,397,457,323,64,223,395,455,674,680,678,676,27,555,214,84,483,556,25,212,82,484,26,554,213,83,482,23,558,217,87,486,24,559,215,85,487,22,557,216,86,485,18,561,79,209,489,16,562,80,210,490,17,560,81,211,488,564,21,78,208,492,565,19,76,206,493,563,20,77,207,491,690,691,688,692 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#a559a3aef5c48d7617a1f37068ce834508ecbb6c78b3262065881b6dd2cda018, 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 19:43:27 · history