Equation 677 Database

← all  ·  ← by size  ·  ← size 321

Magma 468a35a79af0…

magma 468a35a79af0
Size
321
Isomorphism class hash
468a35a79af08731f1b2ea6b83747280e6f2a24ea22aca723741ab20b3a3b06f
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 22:27:40
Display reorder
300,165,46,64,30,111,112,47,166,65,31,45,113,164,63,29,114,167,48,60,33,168,115,49,61,220,231,236,223,62,32,109,170,51,56,28,110,171,52,57,26,55,108,169,50,27,173,106,53,58,24,174,107,54,59,25,172,230,224,225,221,303,313,314,302,183,276,279,277,278,282,280,181,283,281,284,286,182,287,285,290,186,288,291,289,184,294,292,295,293,298,185,296,299,297,271,178,269,270,268,275,179,273,274,272,266,267,180,264,265,177,255,253,254,252,175,259,257,258,256,176,263,261,262,260,320,318,319,317,41,75,85,150,249,242,227,222,86,151,74,132,40,84,152,208,43,71,81,153,44,217,72,82,154,133,42,73,83,155,130,39,67,77,148,131,37,68,78,149,76,129,38,66,147,35,127,69,79,145,36,128,70,80,146,34,233,226,228,235,307,311,308,310,92,192,13,16,100,101,193,90,11,14,194,102,91,12,15,103,88,195,9,19,89,104,196,10,17,105,87,197,8,18,98,211,190,214,213,99,216,191,22,20,206,97,94,189,210,93,95,187,246,247,248,229,237,239,240,241,96,188,7,21,301,316,304,315,203,139,4,158,121,122,140,201,5,159,141,123,202,6,160,124,199,142,3,161,200,125,143,2,162,126,198,144,1,163,119,212,137,215,218,120,219,138,23,157,207,118,205,136,209,204,116,134,245,250,251,232,234,238,243,244,117,135,0,156,305,312,306,309 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#3866b47acdf4717a31e27879d6448be53ada0b89c1671a7aec66e55c44000764, 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 22:27:40 · history