Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 7ebbbca1634d…

magma 7ebbbca1634d
Size
705
Isomorphism class hash
7ebbbca1634ded26a775934d02c631edee49a4fb1ce5b2c12753ac3aa20461f2
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 21:46:23
Display reorder
660,437,215,473,150,597,151,213,438,474,598,214,152,436,472,596,440,153,211,476,600,441,154,212,477,601,439,155,210,475,599,206,443,148,479,603,204,444,149,480,604,205,442,147,478,602,209,446,144,482,606,447,207,145,483,607,445,208,146,481,605,665,667,671,669,56,609,71,23,485,21,610,54,69,486,608,22,55,70,484,59,19,612,67,488,57,20,613,68,489,58,18,611,66,487,615,51,14,62,491,616,52,12,60,492,614,53,13,61,490,618,50,17,65,494,48,619,15,63,495,49,617,16,64,493,685,687,686,691,461,585,239,179,413,177,586,462,237,414,584,178,460,238,412,464,175,588,235,416,465,176,589,236,417,463,174,587,234,415,591,467,170,230,419,592,468,168,228,420,590,466,169,229,418,594,470,173,233,422,471,595,171,231,423,469,593,172,232,421,666,672,664,670,365,553,449,72,352,73,554,366,450,353,552,74,364,448,354,368,75,556,452,355,369,76,557,453,356,367,77,555,451,357,559,371,78,455,358,560,372,79,456,359,558,370,80,454,360,562,374,81,458,361,375,563,82,459,362,373,561,83,457,363,676,678,674,680,377,317,281,95,529,93,318,378,282,530,316,94,376,280,528,380,91,320,284,532,381,92,321,285,533,379,90,319,283,531,323,383,86,287,535,324,384,84,288,536,322,382,85,286,534,326,386,89,290,538,387,327,87,291,539,385,325,88,289,537,663,661,668,662,425,621,389,217,167,218,622,426,390,165,620,216,424,388,166,428,220,624,392,163,429,221,625,393,164,427,219,623,391,162,627,431,223,395,158,628,432,224,396,156,626,430,222,394,157,630,434,226,398,161,435,631,227,399,159,433,629,225,397,160,695,694,699,700,577,277,512,264,253,265,278,578,513,254,279,263,576,511,252,580,260,276,508,256,581,261,274,509,257,579,262,275,510,255,272,583,270,515,259,647,646,271,644,645,273,582,269,514,258,653,655,266,652,654,659,657,267,656,658,651,648,268,649,650,704,702,703,701,565,497,97,333,517,331,498,566,98,518,496,332,564,96,516,568,329,500,100,520,569,330,501,101,521,567,328,499,99,519,503,571,339,103,523,504,572,337,104,524,502,570,338,102,522,506,574,335,106,526,575,507,336,107,527,573,505,334,105,525,698,693,697,696,141,10,401,314,199,315,11,142,402,200,9,313,143,400,198,140,310,6,404,202,138,311,7,405,203,139,312,8,403,201,0,132,305,407,197,2,133,306,408,195,1,134,304,406,196,4,135,308,410,193,136,5,309,411,194,137,3,307,409,192,679,677,681,684,111,31,633,38,341,36,32,112,634,342,30,37,113,632,340,110,41,34,636,344,108,39,35,637,345,109,40,33,635,343,29,117,44,639,347,27,118,42,640,348,28,119,43,638,346,25,116,47,642,350,114,26,45,643,351,115,24,46,641,349,682,683,675,673,296,187,541,246,130,247,188,297,542,131,186,248,295,540,129,292,249,190,544,126,293,250,191,545,127,294,251,189,543,128,185,302,244,547,121,183,303,245,548,122,184,301,243,546,120,181,298,240,550,124,299,182,241,551,125,300,180,242,549,123,692,688,689,690 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#f3708acaf97ab90d0e627f94c9229dfefc0b06412aed9a05696d0ed9b4a78cdc, 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 21:46:24 · history