Equation 677 Database

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Magma 2316e4061daf…

magma 2316e4061daf
Size
321
Isomorphism class hash
2316e4061daf1f6bbee72bad5eeae3977355d4df6c16cb8a93ecf3dcc5c015f0
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 22:50:43
Display reorder
320,288,290,289,293,291,292,296,294,295,299,297,298,52,53,51,48,49,50,58,59,57,54,55,56,0,2,1,4,5,3,7,8,6,10,11,9,14,12,13,17,15,16,20,18,19,23,21,22,172,173,171,168,169,170,178,179,177,174,175,176,302,308,311,313,67,66,68,69,70,71,64,65,63,60,61,62,103,104,102,106,107,105,101,99,100,97,98,96,114,115,116,117,118,119,112,113,111,108,109,110,92,90,91,95,93,94,87,88,89,86,84,85,74,72,73,77,75,76,80,78,79,83,81,82,316,318,317,319,215,214,213,210,211,212,205,206,204,208,209,207,224,222,223,227,225,226,219,220,221,218,216,217,187,188,186,190,191,189,185,183,184,181,182,180,201,202,203,200,198,199,192,193,194,195,196,197,128,126,127,131,129,130,123,124,125,122,120,121,303,307,305,312,261,263,262,259,260,258,254,252,253,257,255,256,267,268,269,266,264,265,273,274,275,272,270,271,239,237,238,235,236,234,230,228,229,233,231,232,241,242,240,244,245,243,247,248,246,250,251,249,141,142,143,140,138,139,132,133,134,135,136,137,300,310,306,315,144,146,145,149,147,148,152,150,151,155,153,154,159,160,161,158,156,157,165,166,167,164,162,163,31,32,30,34,35,33,29,27,28,25,26,24,45,46,47,44,42,43,36,37,38,39,40,41,284,282,283,287,285,286,279,280,281,278,276,277,301,309,304,314 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#b841b444f6b6a6329111833cc0cf1c9cdaf118d6968b1c3e99c4136ce1352ec2, M = {64} 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 22:50:44 · history