Equation 677 Database

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Magma b3844a2bbc80…

magma b3844a2bbc80
Size
321
Isomorphism class hash
b3844a2bbc80c9fb1ca76c02ed8b9a702cba6cde4fef8600e121187c6c9e0de0
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 22:54:45
Display reorder
300,3,201,102,10,218,4,202,100,11,219,5,203,9,217,101,200,6,98,13,214,198,7,99,14,215,199,8,97,12,216,207,18,93,19,211,208,21,91,20,212,15,209,17,92,210,206,1,96,245,246,204,0,94,250,251,205,2,95,16,213,310,311,316,315,258,259,106,257,256,261,262,107,260,263,253,254,252,255,108,270,268,105,269,271,274,272,103,273,275,266,264,104,265,267,282,281,112,280,283,286,284,113,285,287,276,278,277,114,279,294,293,111,292,295,298,296,109,297,299,290,289,110,288,291,318,317,319,320,170,51,119,27,59,168,49,120,25,60,169,50,26,58,118,47,173,115,23,62,48,171,116,24,63,46,172,117,22,61,57,165,125,33,65,55,166,126,31,66,32,56,167,124,64,53,164,121,29,68,54,162,122,30,69,52,163,123,28,67,303,301,304,302,156,73,35,146,85,154,74,36,147,86,155,75,145,87,34,72,152,38,149,88,70,153,39,150,89,71,151,37,148,90,79,160,41,144,83,80,158,42,142,84,143,81,159,40,82,78,247,44,140,244,76,248,45,141,249,77,157,43,139,161,314,312,313,309,233,187,128,226,180,234,188,129,227,181,232,186,228,182,127,190,236,131,229,183,191,237,132,230,184,189,235,130,231,185,193,239,134,224,178,194,240,135,225,179,223,192,238,133,177,196,242,137,220,174,197,243,138,221,175,195,241,136,222,176,306,305,307,308 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#bf96e9533ef77c4b1918ac824d690467af6cf34f1d8a49dfc9562b509f0b1543, 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 22:54:46 · history