Equation 677 Database

← all  ·  ← by size  ·  ← size 321

Magma c034f81cb5fa…

magma c034f81cb5fa
Size
321
Isomorphism class hash
c034f81cb5fae5b39b3bedf41174f1defaa3de9d58fbe9a5c520e41e742e6130
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 22:20:52
Display reorder
300,185,2,83,166,33,183,3,84,164,34,184,0,85,165,35,187,42,86,215,207,186,43,87,167,240,248,220,225,168,36,180,45,88,161,37,181,46,89,162,38,182,44,90,163,39,48,179,91,160,40,208,217,92,159,41,47,247,243,232,219,313,302,310,315,284,287,196,285,286,277,279,197,276,278,281,283,198,280,282,297,299,199,296,298,289,291,200,288,290,293,295,201,292,294,264,267,194,265,266,268,271,195,269,270,272,275,193,273,274,263,260,190,261,262,255,252,191,253,254,259,257,192,256,258,320,317,318,319,121,131,4,106,223,229,244,236,104,68,120,130,8,105,210,212,134,10,109,69,122,132,11,107,70,123,133,9,108,71,50,127,7,101,66,51,128,5,102,67,49,129,6,103,65,126,52,12,211,209,124,53,13,100,64,125,241,237,226,222,305,316,308,307,175,60,14,155,146,173,58,15,153,144,174,59,16,154,145,178,63,17,158,149,176,61,18,156,147,177,62,19,157,148,171,55,20,214,189,216,56,204,151,218,172,57,23,152,188,54,170,21,246,234,242,233,238,231,249,221,169,22,150,1,312,311,301,314,79,96,28,116,140,77,94,29,114,138,78,95,27,115,139,82,99,24,119,143,80,97,25,117,141,81,98,26,118,142,74,202,31,111,136,75,203,32,112,137,76,235,206,113,213,93,73,205,228,245,251,224,239,227,230,250,72,30,110,135,306,309,304,303 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#02a5eb7a1dc0484d80c271e9dde4b7cc0db9de7edd8cff390e9bbef93843b6b3, 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 22:20:53 · history