Equation 677 Database

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Magma 849bd8894373…

magma 849bd8894373
Size
321
Isomorphism class hash
849bd889437321e1772f889d946475468aa0f28828bc1c58526ad8b541e7448a
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 22:22:08
Display reorder
300,107,146,245,49,185,105,144,243,50,183,145,244,48,106,184,149,103,241,52,181,147,104,242,53,182,148,102,240,51,180,98,251,55,152,191,96,249,56,150,189,97,250,54,151,190,101,247,58,155,187,99,248,59,153,188,100,246,57,154,186,313,307,311,306,273,239,272,275,274,264,237,265,267,266,238,269,271,268,270,235,256,257,259,258,236,260,261,263,262,234,252,253,255,254,297,296,298,230,299,288,289,290,228,291,292,293,295,229,294,280,281,282,233,283,285,284,286,231,287,276,277,278,232,279,320,318,319,317,85,70,39,31,164,86,71,40,32,162,69,41,30,84,163,66,88,38,34,167,67,89,36,35,165,68,87,37,33,166,91,45,29,61,159,92,46,27,62,160,90,47,28,60,161,94,44,25,64,158,95,42,26,65,156,93,43,24,63,157,316,305,310,308,124,22,76,143,115,125,23,77,141,116,21,75,142,123,114,18,120,72,139,118,19,121,73,140,119,20,122,74,138,117,130,82,134,13,113,131,83,132,14,111,129,81,133,12,112,126,78,137,16,109,127,79,135,17,110,128,80,136,15,108,315,302,309,301,214,8,174,226,198,215,6,175,227,199,7,176,225,213,200,11,210,177,222,201,9,211,178,223,202,10,212,179,224,203,205,172,217,3,196,206,173,218,4,197,204,171,216,5,195,208,168,220,2,192,209,169,221,1,193,207,170,219,0,194,314,304,312,303 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#1c6b3e96bd585e9e8fd52e93592fcd11cb6c83a04227bfcba3bf653b0809cf1c, 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 22:22:09 · history