Equation 677 Database

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Magma 896d326c7095…

magma 896d326c7095
Size
321
Isomorphism class hash
896d326c7095ce8c315d1c43fd3c3ae2719fd07f944c1528ac772de42d1d062c
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 23:00:21
Display reorder
300,150,182,48,159,131,151,180,49,160,132,152,181,50,161,133,184,51,162,227,230,183,153,52,163,244,248,231,211,164,134,157,46,148,177,129,47,149,178,158,130,45,147,179,156,128,145,44,176,154,126,229,210,175,155,127,146,240,247,232,226,315,311,309,312,278,277,61,279,276,282,281,59,283,280,286,285,60,287,284,288,64,291,289,290,293,294,62,295,292,297,298,63,299,296,271,56,270,268,269,57,274,272,275,273,58,266,265,267,264,254,55,252,255,253,258,53,256,259,257,262,54,260,263,261,318,317,319,320,121,98,21,86,223,225,243,236,87,111,122,99,20,88,224,219,17,85,112,123,100,124,18,83,113,101,125,19,84,114,90,15,119,96,3,13,120,97,91,1,14,118,95,92,2,115,22,93,218,204,116,16,94,89,0,117,237,242,217,205,305,308,307,302,139,4,32,169,188,140,5,30,170,189,141,6,31,171,190,7,28,172,191,142,8,143,29,173,192,9,144,27,174,193,167,24,137,206,187,209,138,207,168,235,23,136,10,166,186,135,26,11,233,249,228,238,208,246,234,245,25,12,165,185,313,310,316,314,105,77,36,199,68,106,78,37,197,69,107,79,38,198,70,80,35,195,71,108,81,109,33,196,72,82,110,34,194,73,203,41,103,75,66,42,104,76,201,67,43,222,216,202,213,102,40,214,251,212,220,239,215,250,241,221,39,74,200,65,303,306,301,304 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#ef4a4f27352a122a7b1088a6208971ffd57fb3858716fe27bd37fbc92d64744c, 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 23:00:22 · history