Equation 677 Database

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Magma e382507058b7…

magma e382507058b7
Size
595
Isomorphism class hash
e382507058b74c842fc34edeb29c939cf90c31bf2cde8de331d84594869c3f77
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 23:19:09
Display reorder
27,26,28,29,24,25,131,130,132,133,128,129,420,422,421,423,424,425,472,471,473,470,469,468,477,479,478,476,475,474,532,531,540,571,551,268,269,168,270,271,213,182,46,47,48,49,45,42,41,43,44,39,40,2,1,3,217,216,0,219,218,174,175,4,5,141,140,142,143,144,237,204,252,205,253,206,203,235,190,236,191,234,189,177,22,18,19,20,21,318,320,319,323,321,322,353,352,351,350,348,349,386,385,384,388,389,387,400,399,401,397,398,396,356,355,354,359,357,358,442,441,443,439,440,438,507,509,508,504,505,506,538,547,517,527,525,526,523,564,550,575,587,553,593,549,572,558,96,97,98,99,94,95,56,61,57,58,59,60,108,107,109,104,105,106,113,112,114,115,110,111,118,117,119,120,121,116,13,12,14,15,16,220,250,161,251,249,201,202,222,221,17,223,224,176,192,153,154,155,151,152,463,462,464,467,466,465,500,498,499,503,501,502,337,336,338,339,340,341,342,344,343,345,346,347,461,460,459,458,457,456,304,303,305,301,302,300,429,431,430,426,427,428,536,529,530,522,520,521,546,569,567,554,586,582,563,579,577,576,10,11,6,7,8,9,92,91,93,88,89,90,82,87,83,84,85,86,136,135,137,138,139,134,72,71,67,68,69,70,35,38,36,37,34,274,280,169,281,277,272,273,276,279,165,278,275,261,228,62,63,64,65,66,390,392,391,395,393,394,450,451,452,454,455,453,335,334,333,331,332,330,402,404,403,405,406,407,292,291,293,289,290,288,282,283,284,286,287,285,435,437,436,432,433,434,537,519,516,510,514,515,513,583,557,556,594,561,548,555,590,559,122,123,124,125,126,127,167,267,211,265,212,266,185,188,232,186,233,187,241,195,196,157,158,159,103,102,100,101,230,231,162,255,256,207,208,254,172,214,173,215,171,170,246,199,247,200,248,198,197,245,242,160,243,244,297,299,298,296,294,295,409,408,410,412,413,411,447,449,448,446,444,445,372,374,373,375,376,377,381,383,382,378,379,380,481,482,480,483,484,485,492,494,493,495,496,497,541,545,533,518,534,535,524,581,565,588,560,592,568,584,585,566,54,55,50,51,52,53,164,259,260,163,257,258,209,210,262,263,166,264,229,183,184,73,74,75,33,32,30,31,181,227,226,225,178,179,180,23,147,146,148,149,150,145,78,77,79,80,81,76,156,193,238,239,240,194,329,328,327,325,326,324,487,488,486,489,490,491,309,311,310,308,306,307,312,314,313,315,316,317,419,418,417,416,414,415,366,368,367,369,370,371,361,360,362,364,365,363,539,528,543,512,542,511,544,570,552,562,578,589,573,580,574,591 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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, 5, B) with E = magma#b1cd85d3b2010871ff4296ca3922edaff9632ccb3821306d9c0360a13ac5958c, M = the submagma generated by {12, 48} (35 elements) in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. 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(5, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + 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: 85.

last edited by qawbecrdtey at 2026-10-08 23:19:10 · history