Equation 677 Database

← all  ·  ← by size  ·  ← size 321

Magma 05d7da0be4b6…

magma 05d7da0be4b6
Size
321
Isomorphism class hash
05d7da0be4b67dc4955c38f4b38eb8c3f3ee0b05121688e2647ec200c23db9ee
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 22:45:34
Display reorder
300,197,125,114,21,41,126,22,198,112,39,23,124,196,113,40,200,128,117,20,37,115,129,201,18,38,199,127,116,19,36,131,203,120,12,47,132,204,118,13,45,130,202,119,14,46,206,134,123,15,43,207,135,121,16,44,205,133,122,17,42,301,302,311,305,259,257,87,258,256,260,261,262,85,263,253,252,254,86,255,270,269,83,268,271,84,273,274,272,275,266,265,82,264,267,280,282,78,281,283,285,286,76,284,287,276,278,77,277,279,294,292,81,293,295,298,297,79,296,299,290,288,80,289,291,319,317,320,318,232,224,210,137,2,222,138,233,208,1,136,223,231,209,0,228,227,213,140,5,211,225,229,141,3,230,226,212,139,4,220,235,216,143,8,238,239,214,144,6,221,234,215,142,7,247,246,219,146,11,251,250,217,147,9,243,242,218,145,10,307,303,314,316,111,91,53,149,167,92,150,109,51,168,148,93,110,52,166,107,90,49,152,170,50,88,108,153,171,106,89,48,151,169,97,102,59,155,165,98,100,57,156,163,99,101,58,154,164,105,96,55,158,161,103,94,56,159,162,104,95,54,157,160,308,306,304,312,179,73,30,61,185,74,62,180,31,186,60,75,178,32,184,182,72,33,64,188,34,70,183,65,189,181,71,35,63,187,69,177,28,67,191,236,175,29,237,192,68,176,27,66,190,173,245,24,244,194,174,249,25,248,195,172,241,26,240,193,315,310,309,313 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#966159413732cc97ab9cbe48ea19b17c045c0e7dae7d4f88fdd62e86aa428734, 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 22:45:35 · history