Equation 677 Database

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Magma 5d386f1de810…

magma 5d386f1de810
Size
321
Isomorphism class hash
5d386f1de810f25ff055ad4291c818513733f63874980da7daac114a4011cd6d
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 22:49:17
Display reorder
300,3,80,180,64,85,4,65,78,181,86,5,63,79,179,84,76,2,176,60,81,1,77,177,61,82,0,75,178,62,83,9,233,234,70,91,237,10,238,71,92,11,103,185,69,90,74,8,182,66,87,72,6,183,67,88,73,7,184,68,89,305,304,313,316,242,268,269,270,271,240,274,272,273,275,241,267,265,264,266,253,245,252,254,255,243,257,256,258,259,244,261,260,263,262,248,292,293,294,295,296,246,297,299,298,247,289,288,291,290,277,251,276,278,279,280,249,281,282,283,284,250,285,286,287,318,319,317,320,47,104,118,212,224,45,213,105,116,225,46,211,106,117,223,107,43,121,208,220,44,108,119,209,221,42,109,120,210,222,38,110,124,218,230,111,36,122,219,231,37,112,123,217,229,113,41,127,214,226,114,39,125,215,227,115,40,126,216,228,311,309,301,302,51,195,200,97,28,52,98,193,201,29,53,96,194,199,27,191,50,196,93,24,48,192,197,94,25,49,190,198,95,26,57,235,206,232,34,239,58,207,236,35,59,186,205,102,33,189,56,202,99,30,187,54,203,100,31,188,55,204,101,32,303,314,307,315,12,140,154,131,168,13,132,141,152,169,14,133,142,153,167,143,15,157,130,164,16,144,155,128,165,17,145,156,129,166,18,146,160,137,174,147,19,158,138,175,20,148,159,139,173,149,21,163,136,170,150,22,161,134,171,151,23,162,135,172,306,312,310,308 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#a72914db9cdb367a789c5baa8372a3d5fedd55bc0a2411348ad61481f273a706, 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 22:49:18 · history