Equation 677 Database

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Magma d1a3f6eadfb7…

magma d1a3f6eadfb7
Size
321
Isomorphism class hash
d1a3f6eadfb7825c60dc1510ac45d27489981628abb1d7deabde9c03559fb77e
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 22:54:37
Display reorder
300,178,61,179,88,98,181,180,89,99,59,182,60,183,90,100,57,185,184,216,218,58,187,186,91,243,240,234,233,92,101,174,175,54,86,96,87,176,177,52,97,173,172,53,85,95,170,171,56,83,93,232,212,55,84,94,169,249,239,215,217,306,307,315,313,279,192,277,276,278,281,283,280,282,190,285,191,287,284,286,195,288,291,289,290,193,293,295,292,294,194,297,299,296,298,269,271,198,268,270,272,273,275,196,274,264,267,197,265,266,255,252,201,253,254,259,256,199,257,258,263,261,200,260,262,320,317,318,319,78,42,67,118,208,214,242,246,25,43,68,44,79,119,207,213,69,80,120,22,45,70,81,121,23,46,71,82,122,24,65,76,47,116,28,117,66,77,48,29,64,75,49,115,27,72,62,50,223,209,73,63,51,114,26,74,241,238,224,210,309,316,305,304,3,36,141,8,163,142,4,9,164,34,143,35,2,10,165,32,140,1,7,166,33,138,0,6,167,31,139,189,188,168,133,104,40,204,162,205,134,220,38,231,135,103,39,5,161,102,136,30,237,230,244,227,236,211,248,219,137,37,41,160,314,311,312,301,158,107,11,127,146,12,159,128,144,105,13,106,157,129,145,110,14,154,130,149,108,15,155,131,147,109,16,156,132,148,17,202,112,125,151,126,18,203,111,150,19,235,221,124,228,153,20,222,225,247,251,206,245,226,229,250,21,113,123,152,310,303,308,302 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#be22598f61f867b223264cf52ecf408910eea148415a700aef96392fba43b30a, 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 22:54:38 · history