Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 0b3d5470fd2c…

magma 0b3d5470fd2c
Size
705
Isomorphism class hash
0b3d5470fd2cda4454a61aed6b2862cd9d13325471dc14c503c7c83459d87701
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 16:56:04
Display reorder
660,312,221,491,515,20,313,513,219,489,18,220,514,314,490,19,315,217,487,511,23,316,218,488,512,21,317,216,486,510,22,497,212,310,521,15,495,210,311,519,16,496,211,309,520,17,215,493,306,517,14,213,494,307,518,12,214,492,308,516,13,668,672,664,667,503,420,147,172,479,501,173,421,148,477,422,171,502,149,478,499,423,146,168,475,500,424,144,169,476,498,425,145,170,474,138,418,509,163,485,139,419,507,164,483,140,417,508,162,484,414,141,505,166,481,415,142,506,167,482,416,143,504,165,480,691,687,688,685,443,205,177,250,244,441,251,206,178,245,204,249,442,179,243,439,208,176,246,240,440,209,174,247,241,438,207,175,248,242,183,203,449,256,235,184,201,447,257,236,185,202,448,255,234,199,182,445,252,238,200,180,446,253,239,198,181,444,254,237,662,670,665,661,431,105,601,602,52,429,597,106,598,53,107,599,430,600,51,427,104,593,594,55,428,102,595,596,56,426,103,591,592,54,613,111,437,614,50,610,112,435,609,48,611,113,436,612,49,110,605,433,606,46,108,607,434,608,47,109,604,432,603,45,681,673,675,680,467,68,629,395,527,465,393,66,627,525,67,394,466,628,526,463,64,625,391,523,464,65,626,392,524,462,63,624,390,522,635,59,473,401,533,633,57,471,399,531,634,58,472,400,532,62,631,469,397,529,60,632,470,398,530,61,630,468,396,528,663,669,666,671,322,195,371,224,334,323,222,196,369,335,197,223,321,370,333,318,194,367,227,330,319,192,368,225,331,320,193,366,226,332,377,186,328,230,340,375,187,329,228,341,376,188,327,229,339,189,373,324,233,336,190,374,325,231,337,191,372,326,232,338,699,700,693,695,74,4,550,620,39,72,618,5,551,40,3,619,73,549,41,70,1,546,616,42,71,0,547,617,43,69,2,548,615,44,658,8,656,659,657,651,9,648,650,649,654,7,652,655,653,6,552,76,622,36,11,553,77,623,37,10,554,75,621,38,704,702,703,701,539,120,560,359,346,537,357,121,558,347,122,358,538,559,345,535,123,556,355,342,536,124,557,356,343,534,125,555,354,344,566,118,545,365,352,564,119,543,363,353,565,117,544,364,351,114,562,541,361,348,115,563,542,362,349,116,561,540,360,350,694,697,696,698,288,99,25,584,296,289,582,100,26,294,101,583,290,24,295,291,98,28,580,299,292,96,29,581,297,293,97,27,579,298,31,90,286,590,302,32,91,287,588,300,30,92,285,589,301,93,34,282,586,305,94,35,283,587,303,95,33,284,585,304,679,678,677,684,80,132,407,455,641,78,453,133,405,639,134,454,79,406,640,83,135,403,451,637,81,136,404,452,638,82,137,402,450,636,413,130,86,461,647,411,131,84,459,645,412,129,85,460,646,126,409,89,457,643,127,410,87,458,644,128,408,88,456,642,676,683,682,674,383,156,274,262,572,381,263,157,275,570,158,261,382,273,571,379,159,270,258,568,380,160,271,259,569,378,161,272,260,567,280,154,389,268,578,281,155,387,269,576,279,153,388,267,577,150,276,385,264,574,151,277,386,265,575,152,278,384,266,573,689,692,686,690 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#48d4131c324a99301720abcc6dab4afc68cf81d40922963883b47bf0604d0986, 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 16:56:05 · history