Equation 677 Database

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Magma dbf907b1a347…

magma dbf907b1a347
Size
321
Isomorphism class hash
dbf907b1a3474539f903a97b727c4aee50b83a340ed3d3fa324067d53b8201e5
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 22:21:00
Display reorder
300,125,22,134,142,100,123,23,132,143,101,124,21,133,141,99,121,18,130,233,229,19,122,131,201,197,120,20,129,217,213,128,117,140,148,106,126,118,138,149,107,127,119,139,147,105,215,216,136,144,102,231,232,137,145,103,199,200,135,146,104,308,305,304,314,269,246,268,271,270,273,247,272,275,274,264,248,265,266,267,253,249,252,255,254,250,257,256,259,258,261,251,260,262,263,292,244,293,295,294,296,245,297,298,299,288,243,289,290,291,240,276,277,279,278,241,280,281,283,282,242,284,285,287,286,317,319,320,318,80,67,96,8,192,78,68,97,6,208,79,66,98,7,225,228,63,95,4,1,64,196,93,5,0,212,65,94,3,2,83,58,87,172,175,81,59,88,173,176,82,57,89,171,174,61,86,90,235,236,62,84,91,203,204,60,85,92,219,220,311,313,301,302,181,27,73,154,112,182,28,74,155,113,180,29,72,153,111,177,26,69,150,108,24,178,70,151,109,179,25,71,152,110,221,33,211,234,214,237,34,227,202,230,205,35,195,218,198,32,183,75,156,114,30,184,76,157,115,31,185,77,158,116,309,306,316,303,163,43,189,45,10,164,44,190,46,11,162,42,191,47,9,159,39,188,48,13,40,160,186,49,14,161,41,187,50,12,169,194,207,51,193,170,210,223,52,209,168,226,238,53,224,37,165,239,54,16,38,166,206,55,17,36,167,222,56,15,315,312,310,307 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#05c0aaa7a3560fa146ae1951a40d178d675f2688aa4f7579703e2b967da3180b, 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 22:21:01 · history