Equation 677 Database

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Magma 98f5dbe1b917…

magma 98f5dbe1b917
Size
321
Isomorphism class hash
98f5dbe1b91732193001962b02d0ac1b407b93efcdbfb0f28808a6d8067d1586
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 22:59:48
Display reorder
300,11,71,86,163,56,12,72,87,165,57,13,73,166,88,58,10,74,89,169,59,2,75,90,171,225,221,227,229,173,60,17,69,84,158,54,18,70,85,160,55,19,68,83,157,53,16,66,81,155,51,14,67,82,0,52,15,226,228,238,224,306,301,303,315,46,278,277,276,279,47,283,281,280,282,45,287,284,285,286,49,290,289,288,291,50,295,293,292,294,48,299,297,296,298,44,271,268,269,270,42,275,272,273,274,43,267,265,264,266,40,254,252,253,255,41,258,256,257,259,39,263,261,260,262,318,319,317,320,94,148,123,4,222,230,236,233,1,29,95,149,124,125,30,93,150,126,127,33,91,151,128,129,31,92,152,130,131,32,99,146,121,5,36,100,147,122,6,34,101,145,120,7,35,98,143,118,8,38,96,144,119,9,37,97,235,232,220,223,314,310,313,309,65,184,112,195,193,192,182,110,188,79,64,183,189,111,80,62,180,108,186,77,63,181,109,187,78,61,179,107,185,76,210,176,104,219,217,216,174,102,207,205,204,175,103,213,211,198,178,106,251,249,248,239,231,245,243,242,177,105,201,199,307,304,305,308,3,137,162,190,194,191,138,164,23,116,25,139,24,167,117,26,140,168,21,114,27,141,170,22,115,28,142,172,20,113,208,135,159,215,218,214,136,161,203,206,202,134,156,209,212,196,132,154,247,250,246,234,237,240,244,241,133,153,197,200,312,316,311,302 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#e3fb677801a83abf4523d8c5dab7d3c82647015c862300302a3edde7221f68e9, 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 22:59:49 · history