Equation 677 Database

← all  ·  ← by size  ·  ← size 595

Magma b456d8ac9858…

magma b456d8ac9858
Size
595
Isomorphism class hash
b456d8ac9858fd00378e6dcca319877b657695b42416c7879fcc072db7210c7a
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
2026-10-06 14:30:16
Display reorder
310,309,311,306,307,308,369,368,370,382,366,367,432,433,431,436,434,435,399,401,400,396,397,398,403,402,404,406,407,405,511,525,515,519,590,206,189,188,191,192,190,203,67,65,66,204,205,207,202,198,199,200,201,42,47,43,44,45,46,330,335,331,332,333,334,160,159,161,162,163,158,251,250,246,247,248,249,283,282,284,285,286,287,23,22,18,19,20,21,7,6,8,9,10,11,1,5,0,2,3,4,352,351,353,349,350,348,354,356,355,358,359,357,411,410,409,412,413,414,440,501,500,509,502,503,408,485,456,483,455,484,518,538,512,513,529,571,594,557,582,575,539,555,554,574,558,572,312,314,313,316,317,315,73,72,68,69,70,71,88,87,89,90,91,86,39,38,40,41,36,37,265,264,266,267,268,269,98,103,99,100,101,102,171,170,172,173,174,175,242,241,243,244,245,240,281,280,276,277,278,279,131,130,132,133,128,129,255,254,256,257,252,253,494,496,495,467,468,493,488,487,506,461,460,423,469,471,470,473,474,472,340,339,341,337,338,336,424,489,462,491,463,490,535,531,528,516,517,556,579,545,573,559,547,562,581,591,577,542,215,217,216,219,214,218,209,208,210,211,212,213,157,156,152,153,154,155,176,181,177,178,179,180,95,94,96,97,92,93,150,149,151,146,147,148,299,298,294,295,296,297,168,167,169,164,165,166,182,187,183,184,185,186,29,28,24,25,26,27,293,292,288,289,290,291,420,419,418,417,415,416,364,363,365,362,360,361,344,346,347,342,343,345,498,497,499,442,508,439,476,383,477,507,475,441,534,537,526,536,532,553,565,551,564,587,585,584,576,589,583,566,105,107,106,109,104,108,195,194,196,197,237,193,232,239,233,234,235,236,62,61,63,64,59,60,136,135,137,138,139,134,123,122,124,125,126,127,49,48,50,51,52,53,325,324,326,327,328,329,303,302,304,305,300,301,118,117,119,120,121,116,221,220,222,223,224,225,374,376,375,371,372,373,379,378,377,380,381,443,459,458,422,486,421,457,392,391,390,395,393,394,386,385,505,478,504,384,527,530,524,521,510,570,586,549,593,543,541,548,588,546,567,563,35,31,30,33,34,32,57,56,54,238,58,55,263,262,258,259,260,261,74,79,75,76,77,78,81,80,82,83,84,85,112,111,113,114,115,110,275,274,270,271,272,273,323,322,318,319,320,321,226,231,227,228,229,230,141,140,142,143,144,145,17,16,12,13,14,15,492,466,465,438,437,464,448,447,446,449,450,451,454,453,389,482,388,452,430,429,428,427,426,425,387,481,445,479,444,480,522,520,523,514,533,578,561,569,592,580,552,560,568,550,544,540 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#be842e4d65ca083f5f61a36963819b0aa7d50180968070250538ce7f22ff68d2, M = the submagma generated by {66, 84} (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 2026-10-06 14:30:18 · history