Equation 677 Database

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Magma d7728c204efb…

magma d7728c204efb
Size
321
Isomorphism class hash
d7728c204efbfe668d18b7fadca32f9e76d11cfb91b229a06679ff5db9a92e17
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 22:55:08
Display reorder
300,105,26,245,163,4,106,24,243,164,5,107,25,244,162,3,29,104,241,166,1,27,102,242,167,0,28,103,240,165,2,96,251,32,161,10,97,249,30,159,11,98,250,31,160,9,247,99,35,157,6,248,100,33,158,7,246,101,34,156,8,303,304,312,315,273,14,272,275,274,264,12,265,266,267,269,13,268,270,271,17,256,257,259,258,15,260,261,262,263,16,252,253,254,255,296,297,20,299,298,288,289,18,290,291,292,293,19,295,294,281,280,23,282,283,285,284,21,286,287,277,276,22,278,279,319,318,317,320,221,118,168,209,59,219,119,169,207,57,220,117,170,208,58,114,217,171,205,55,115,218,172,206,56,116,216,173,204,54,227,174,109,215,50,225,175,110,213,48,226,176,108,214,49,177,223,112,211,53,178,224,113,212,51,179,222,111,210,52,307,316,311,302,124,183,149,133,69,125,184,147,134,70,123,185,148,132,71,182,120,145,136,68,180,121,146,137,66,181,122,144,135,67,130,155,189,139,60,131,153,190,140,61,129,154,191,138,62,151,126,188,142,63,152,127,186,143,64,150,128,187,141,65,310,301,314,305,74,37,197,233,84,72,38,195,231,85,73,36,196,232,86,40,77,193,229,87,41,75,194,230,88,39,76,192,228,89,80,203,43,239,90,78,201,44,237,91,79,202,42,238,92,199,83,46,235,93,200,81,47,236,94,198,82,45,234,95,309,308,313,306 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#c84e71ca0bd6781f4c1c1e66d375057eb5ddb823e6cd89140cc4ca3da0f421d2, 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 22:55:08 · history