Equation 677 Database

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Magma 7c2bf206df14…

magma 7c2bf206df14
Size
321
Isomorphism class hash
7c2bf206df14a536a1f8f5637ec2d16cceeeed30e75c3f26da6871712ae790ae
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 320) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 22:37:57
Display reorder
315,255,264,275,232,107,10,163,223,108,11,164,222,12,106,162,220,13,105,161,221,233,254,263,274,14,216,156,100,15,217,157,101,16,215,158,102,219,17,159,103,273,234,262,253,218,18,160,104,138,139,140,141,142,143,136,137,286,284,285,287,304,303,308,312,277,292,295,282,5,129,149,214,6,130,150,213,128,9,148,210,126,7,146,211,127,8,147,212,134,206,154,1,283,294,293,276,135,205,155,4,208,133,153,0,209,131,151,2,207,132,152,3,41,42,40,37,38,39,47,48,45,43,44,46,310,302,306,313,124,74,20,35,125,36,75,19,261,240,243,235,34,123,73,22,239,260,242,236,33,122,72,21,28,25,67,117,29,23,68,118,30,24,69,119,237,238,241,259,26,31,70,120,27,32,71,121,65,66,64,61,62,63,144,145,290,288,289,291,305,319,300,314,281,280,278,279,113,84,92,81,114,85,93,80,247,258,250,246,86,115,94,83,87,116,95,82,88,79,96,112,248,245,251,257,89,78,97,111,76,90,98,109,77,91,99,110,244,249,252,256,59,60,58,55,56,57,50,51,52,53,54,49,309,307,301,311,169,178,198,189,170,190,179,199,171,191,180,200,192,172,177,197,193,173,175,195,194,174,176,196,269,271,267,265,270,272,268,266,188,204,184,168,203,185,183,165,201,186,181,166,202,187,182,167,224,225,226,227,228,229,230,231,298,296,297,299,317,316,318,320 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 321 = 1 + 5*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, 5, B) with E = magma#7b4d86832894383b0b7ce3dfc16e526670032b07fced110816f25e14f2157e1a, M = {60} 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, 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: 21.

last edited by qawbecrdtey at 2026-10-01 22:37:57 · history