Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma b4f66c435814…

magma b4f66c435814
Size
705
Isomorphism class hash
b4f66c4358142b24dff986f59d064190a4db37b223fc1c222583f1dc1959fec3
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 21:56:58
Display reorder
660,614,142,452,500,375,612,143,376,450,498,613,141,377,451,499,617,138,374,455,503,615,139,372,453,501,616,140,373,454,502,133,381,447,609,495,134,382,448,610,496,132,383,449,611,497,380,136,446,608,494,378,137,444,606,492,379,135,445,607,493,668,670,672,661,322,31,295,300,191,323,32,189,296,301,321,30,190,294,302,318,34,187,298,303,319,35,188,299,304,320,33,186,297,305,37,182,293,313,306,38,180,291,314,307,36,181,292,312,308,185,40,289,316,309,183,41,290,317,310,184,39,288,315,311,690,688,685,686,464,163,512,66,440,462,164,438,510,67,463,162,439,511,68,467,166,443,515,69,465,167,441,513,70,466,165,442,514,71,161,435,507,459,64,159,436,508,460,65,160,437,509,461,63,434,157,506,458,60,432,158,504,456,61,433,156,505,457,62,671,664,669,667,590,334,200,530,356,588,335,354,198,528,589,333,355,199,529,593,330,359,203,533,591,331,357,201,531,592,332,358,202,532,325,351,195,585,525,326,352,196,586,526,324,353,197,587,527,350,328,194,584,524,348,329,192,582,522,349,327,193,583,523,679,677,681,674,428,253,210,344,416,426,254,414,211,342,427,252,415,212,343,431,256,419,213,347,429,257,417,214,345,430,255,418,215,346,259,411,208,423,339,260,412,209,424,340,258,413,207,425,341,410,262,204,422,338,408,263,205,420,336,409,261,206,421,337,662,663,666,665,404,146,86,368,392,402,144,390,84,366,403,145,391,85,367,407,149,395,89,371,405,147,393,87,369,406,148,394,88,370,152,387,92,399,363,150,388,90,400,364,151,389,91,401,365,386,155,95,398,362,384,153,93,396,360,385,154,94,397,361,697,694,696,695,644,51,646,645,647,638,52,639,637,636,640,53,643,642,641,656,50,659,658,657,649,48,651,650,648,653,49,655,654,652,42,621,54,517,3,43,622,55,518,4,44,623,56,516,5,620,45,57,520,2,618,46,58,521,1,619,47,59,519,0,703,701,702,704,629,245,628,578,217,624,243,218,625,576,626,244,216,627,577,635,241,220,634,581,630,242,221,631,579,633,240,219,632,580,251,223,271,269,573,249,224,272,267,574,250,222,270,268,575,226,247,274,265,572,227,248,275,266,570,225,246,273,264,571,699,698,700,693,602,22,124,12,114,600,23,115,125,13,601,21,116,123,14,605,18,117,120,15,603,19,118,121,16,604,20,119,122,17,28,112,130,597,10,29,113,131,598,11,27,111,129,599,9,108,24,126,596,6,109,25,127,594,7,110,26,128,595,8,684,676,682,678,476,281,554,104,236,474,279,234,552,102,475,280,235,553,103,479,277,239,557,107,477,278,237,555,105,478,276,238,556,106,287,231,549,471,99,285,232,550,472,100,286,233,551,473,101,230,283,548,470,98,228,284,546,468,96,229,282,547,469,97,680,683,675,673,542,75,566,488,168,540,76,169,564,486,541,77,170,565,487,545,74,171,569,491,543,72,172,567,489,544,73,173,568,490,81,174,561,537,483,82,175,562,538,484,83,176,563,539,485,177,80,560,536,482,178,78,558,534,480,179,79,559,535,481,689,692,687,691 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#fd86fc294900b5ccb814b44936109aa3958b6cd4f65ecf12bfe08854715a531f, 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 21:56:59 · history