Equation 677 Database

← all  ·  ← by size  ·  ← size 321

Magma 9bbebee0c1b2…

magma 9bbebee0c1b2
Size
321
Isomorphism class hash
9bbebee0c1b2d9a71d1f05b5c2cd349e66a5bd2834975f549fa0f554cdc58f3f
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 22:21:58
Display reorder
300,77,25,158,232,235,26,239,75,159,236,27,231,76,157,229,93,28,80,154,43,223,29,78,155,220,227,30,79,156,224,96,31,72,149,41,94,32,73,150,42,95,33,74,148,40,34,99,71,152,37,35,97,69,153,38,36,98,70,151,39,306,302,314,313,242,294,293,292,295,299,298,240,296,297,291,290,241,289,288,279,278,245,277,276,283,282,243,280,281,287,286,244,284,285,259,258,248,257,256,262,263,246,261,260,255,254,247,253,252,270,271,251,268,269,274,275,249,273,272,267,266,250,264,265,317,320,319,318,68,82,207,194,218,83,219,66,205,195,81,217,67,206,193,214,85,64,203,190,215,86,65,204,191,216,84,63,202,192,209,88,59,198,185,210,89,57,196,186,208,87,58,197,184,91,212,62,201,188,92,213,60,199,189,90,211,61,200,187,301,304,309,311,10,234,182,171,233,238,237,11,183,169,230,228,12,181,170,1,56,9,178,167,221,222,7,179,168,225,226,8,180,166,44,52,0,173,162,45,50,2,174,160,46,51,3,172,161,55,47,4,176,165,53,48,5,177,163,54,49,6,175,164,308,316,303,315,14,113,146,135,106,114,107,15,147,133,112,108,13,145,134,109,116,17,142,131,110,117,18,143,132,111,115,16,144,130,104,119,20,137,126,105,120,21,138,124,103,118,19,136,125,122,100,23,140,129,123,101,24,141,127,121,102,22,139,128,305,307,312,310 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#198f8683bee40b5fe0cfed42350fb71daef6a15506139cdcf5a71dcf11978025, 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 22:21:59 · history