Equation 677 Database

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Magma 6d7d89e40ea2…

magma 6d7d89e40ea2
Size
321
Isomorphism class hash
6d7d89e40ea29de3545f63a9d3b51a55a66a7554f7072a4b2c39c16320df18ae
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 22:22:30
Display reorder
300,202,201,203,200,198,199,192,193,194,195,196,197,73,74,72,76,77,75,79,80,78,82,83,81,215,213,214,211,212,210,206,204,205,209,207,208,51,52,53,50,48,49,57,58,59,56,54,55,267,268,269,266,264,265,273,274,275,272,270,271,301,309,312,314,131,130,129,126,127,128,121,122,120,124,125,123,143,141,142,139,140,138,134,132,133,137,135,136,154,155,153,150,151,152,145,146,144,148,149,147,167,165,166,163,164,162,158,156,157,161,159,160,113,111,112,109,110,108,119,117,118,115,116,114,317,319,318,320,85,84,86,87,88,89,90,91,92,93,94,95,227,225,226,223,224,222,218,216,217,221,219,220,34,35,33,30,31,32,25,26,24,28,29,27,1,0,2,3,4,5,6,7,8,9,10,11,276,277,278,279,280,281,282,283,284,285,286,287,304,307,306,313,297,299,298,295,296,294,290,288,289,293,291,292,244,245,243,240,241,242,250,251,249,246,247,248,232,233,231,228,229,230,238,239,237,234,235,236,100,101,99,96,97,98,106,107,105,102,103,104,177,178,179,176,174,175,168,169,170,171,172,173,303,311,310,316,66,68,67,71,69,70,63,64,65,62,60,61,260,258,259,263,261,262,255,256,257,254,252,253,21,22,23,20,18,19,12,13,14,15,16,17,184,185,183,180,181,182,190,191,189,186,187,188,36,37,38,39,40,41,42,43,44,45,46,47,302,308,305,315 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#22cb8afe1ff0462b448663f4450c6ce0a1106142be9f7b23381e657feeb5c2cf, M = {62} 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 22:22:31 · history