Equation 677 Database

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Magma d8c7683d9c54…

magma d8c7683d9c54
Size
321
Isomorphism class hash
d8c7683d9c5403d643ca2e18b71964088846d74de82382b6291da0f38b16e2fd
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 22:49:06
Display reorder
300,26,157,174,181,85,158,24,175,182,86,25,156,176,180,84,29,160,177,184,88,27,161,178,185,89,28,159,179,183,87,32,163,187,172,91,30,164,188,173,92,31,162,186,171,90,166,35,190,168,94,167,33,191,169,95,165,34,189,170,93,306,307,312,315,243,257,259,258,256,260,244,262,261,263,245,252,254,253,255,242,269,270,268,271,240,273,274,272,275,241,265,266,264,267,249,281,282,280,283,250,285,286,284,287,251,276,278,277,279,292,248,294,293,295,297,246,298,296,299,288,247,290,289,291,319,320,317,318,146,121,106,110,229,122,144,107,108,230,145,120,105,109,228,149,124,102,113,232,147,125,103,111,233,148,123,104,112,231,152,127,116,97,235,150,128,114,98,236,151,126,115,96,234,130,155,119,100,238,131,153,117,101,239,129,154,118,99,237,302,316,311,301,54,140,63,4,17,138,55,64,5,15,56,139,65,3,16,57,143,62,1,13,58,141,60,0,14,59,142,61,2,12,52,135,10,69,23,53,136,11,70,21,51,137,9,71,22,134,48,6,68,19,132,49,7,66,20,133,50,8,67,18,310,304,314,308,80,195,215,217,37,196,78,213,218,38,79,197,214,216,36,83,194,211,220,40,81,192,212,221,41,82,193,210,219,39,75,201,223,206,43,76,202,224,204,44,77,203,222,205,42,200,74,226,209,46,198,72,227,207,47,199,73,225,208,45,305,309,313,303 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#a559a3aef5c48d7617a1f37068ce834508ecbb6c78b3262065881b6dd2cda018, 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 22:49:07 · history