Equation 677 Database

← all  ·  ← by size  ·  ← size 321

Magma fde42dc4e65d…

magma fde42dc4e65d
Size
321
Isomorphism class hash
fde42dc4e65dd4e1739c6a5af9ffe36edb1d9074d408d4ba7f8ce4b6980a2810
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 22:21:50
Display reorder
300,109,185,71,245,121,110,69,243,122,183,108,184,70,244,120,181,112,67,241,124,182,113,68,242,125,180,111,66,240,123,62,115,191,251,127,116,189,249,60,128,114,190,250,61,126,187,118,247,65,130,188,119,248,63,131,186,117,246,64,129,315,313,301,305,272,273,2,275,274,264,1,266,267,265,268,269,0,270,271,256,257,5,259,258,260,261,3,262,263,252,253,4,254,255,8,297,296,299,298,289,288,290,6,291,293,292,295,7,294,280,281,282,11,283,285,284,286,9,287,276,277,278,10,279,319,317,318,320,34,21,141,221,78,35,142,219,79,22,33,23,143,220,80,20,30,140,217,81,18,31,138,218,82,19,32,139,216,83,132,25,12,227,76,26,13,225,133,77,24,14,226,134,75,15,28,223,135,72,16,29,224,136,73,17,27,222,137,74,308,312,316,302,209,196,85,149,233,207,86,147,231,197,208,195,84,148,232,192,205,88,145,229,193,206,89,146,230,194,204,87,144,228,91,215,202,155,239,213,203,153,92,237,214,201,154,90,238,198,211,151,94,235,199,212,152,95,236,200,210,150,93,234,303,311,307,310,173,160,97,49,37,171,98,50,38,161,172,159,96,48,36,156,169,100,52,40,157,170,101,53,41,158,168,99,51,39,103,179,166,55,43,177,167,56,104,44,178,165,54,102,42,162,175,58,106,46,163,176,59,107,47,164,174,57,105,45,306,314,304,309 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#164604ba66664ae7e7b126fe65d39300d84fb27e5ce614035873663e987c6567, 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 22:21:51 · history