Equation 677 Database

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Magma 7dc7a5004b97…

magma 7dc7a5004b97
Size
321
Isomorphism class hash
7dc7a5004b971c3780078ad0943dc587b57b6b9809cac20589022c0aef6b7236
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 22:27:59
Display reorder
300,52,179,31,196,6,7,180,50,29,194,8,181,51,30,195,9,48,182,34,192,49,10,183,32,193,47,11,184,33,191,58,185,4,249,248,186,5,27,56,200,187,3,28,57,201,1,188,25,54,198,189,0,26,55,199,2,190,24,53,197,314,313,305,304,108,272,275,274,273,264,265,109,266,267,268,269,107,270,271,257,111,256,259,258,112,261,260,262,263,110,253,252,254,255,114,296,297,299,298,289,288,290,115,291,293,292,295,113,294,281,280,282,117,283,284,285,286,118,287,276,277,278,116,279,318,319,317,320,137,17,172,160,39,40,15,138,170,158,38,16,139,171,159,35,140,13,168,156,141,36,14,169,157,142,37,12,167,155,135,23,45,178,166,21,46,176,136,164,22,44,177,134,165,41,19,174,131,162,20,42,175,132,163,43,18,173,133,161,308,310,301,302,150,242,222,208,225,226,240,151,223,209,227,241,149,224,207,228,153,238,221,211,154,229,239,219,212,152,230,237,220,210,148,251,231,213,250,246,232,214,146,205,247,233,215,147,206,234,244,216,144,203,245,235,217,145,204,236,243,218,143,202,316,312,315,306,121,80,100,83,66,67,81,119,98,84,65,82,120,99,85,69,124,79,96,86,122,70,77,97,87,123,68,78,95,88,127,71,64,106,89,72,62,104,125,90,73,63,105,126,91,60,74,102,130,92,75,61,103,128,93,59,76,101,129,94,311,303,307,309 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#3d4915088e45e024e7bce9a29cd7ec921add83e4b04ab0fb3d527eb1a5f02fc2, 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 22:28:00 · history