Equation 677 Database

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Magma 13f955dea8ac…

magma 13f955dea8ac
Size
321
Isomorphism class hash
13f955dea8acff1fa18ba8fb4da32bfcb628e1bdda2268223ccf74d103fb25ec
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 22:37:33
Display reorder
300,159,210,92,101,168,90,211,99,169,160,212,161,91,100,170,158,213,95,97,171,156,214,93,98,172,157,215,94,96,173,208,165,87,107,174,209,166,88,105,175,207,167,89,106,176,164,204,86,103,177,162,205,84,104,178,102,163,206,85,179,315,316,301,302,272,224,273,275,274,264,222,267,266,265,223,269,268,271,270,257,227,256,259,258,261,225,260,263,262,253,226,252,255,254,219,296,297,298,299,220,289,288,290,291,221,293,292,295,294,281,218,280,282,283,284,216,285,286,287,278,277,217,276,279,320,319,318,317,238,38,239,186,114,235,36,187,115,234,37,236,237,188,116,230,41,231,189,117,232,39,233,190,118,229,40,228,191,119,44,251,250,184,112,42,247,246,185,113,43,249,248,183,111,243,47,242,180,108,245,45,244,181,109,182,241,46,240,110,310,309,307,308,58,1,121,137,197,122,0,135,195,59,2,57,120,136,196,54,3,124,133,193,55,4,125,134,194,56,5,123,132,192,6,49,127,143,203,7,50,128,141,201,8,48,126,142,202,52,9,130,139,199,53,10,131,140,200,138,51,11,129,198,311,312,306,303,24,15,61,76,149,62,16,77,147,25,17,26,60,75,148,27,14,64,72,145,28,12,65,73,146,29,13,63,74,144,21,30,67,82,155,22,31,68,83,153,23,32,66,81,154,33,20,70,78,151,34,18,71,79,152,80,35,19,69,150,314,313,304,305 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#70fbce4d1be954c5232f18b8807a18e39f88f6f161a168e0f82db887a05a7819, 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 22:37:34 · history