Equation 677 Database

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Magma 4e31d02c5cb3…

magma 4e31d02c5cb3
Size
321
Isomorphism class hash
4e31d02c5cb332ed6d383d8d10ea4fa61643e547f3bfa0f654ede7e266ef20f2
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 22:49:49
Display reorder
300,177,101,213,109,64,178,65,99,214,110,179,63,100,215,108,60,176,97,212,112,61,174,98,210,113,62,175,96,211,111,107,168,70,204,115,105,169,71,205,116,206,106,170,69,114,171,103,66,207,118,172,104,67,208,119,173,102,68,209,117,309,301,303,307,291,290,288,289,28,294,29,295,292,293,298,27,299,297,296,24,287,286,285,284,25,279,278,276,277,26,283,282,280,281,255,254,34,252,253,258,259,35,256,257,260,263,262,33,261,267,266,30,265,264,271,270,31,269,268,274,275,32,273,272,320,319,317,318,201,54,129,165,140,202,138,55,130,166,203,139,56,131,167,143,200,57,128,164,141,198,58,126,162,142,199,59,127,163,52,192,135,120,156,53,193,136,121,157,122,51,194,137,158,195,48,134,123,159,196,49,132,124,160,197,50,133,125,161,304,306,315,316,189,84,153,225,77,190,75,85,154,226,191,76,86,155,227,73,188,87,152,224,74,186,88,150,222,72,187,89,151,223,90,180,83,144,216,91,181,81,145,217,146,92,182,82,218,183,93,79,147,219,184,94,80,148,220,185,95,78,149,221,305,310,302,308,246,11,247,15,39,249,40,9,248,16,251,41,10,250,17,38,245,7,244,14,36,241,8,240,12,37,243,6,242,13,2,229,45,228,21,1,230,46,231,22,233,0,232,47,23,234,5,44,235,20,237,3,42,236,18,239,4,43,238,19,311,314,313,312 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#b25ea76719ef85ac96ca5a21eaa9f8d56a10b2e0f8b67970c90091297d765387, 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 22:49:50 · history