Equation 677 Database

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Magma c3b29f605cd2…

magma c3b29f605cd2
Size
381
Isomorphism class hash
c3b29f605cd26851739fc07fbe1835512c532cf0384c6180bad5104117907b8a
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:45:21
Display reorder
380,192,187,182,202,207,197,134,120,127,147,137,142,74,72,73,218,75,76,80,81,84,83,227,82,311,307,309,316,313,315,247,237,242,262,252,257,71,213,70,68,69,67,277,267,272,295,282,285,292,87,232,86,85,88,162,152,157,177,167,172,79,1,0,78,223,77,367,343,332,348,357,362,352,338,377,372,193,188,183,203,208,198,132,123,128,148,138,143,7,8,6,216,5,4,90,91,89,93,228,92,325,326,324,328,329,327,248,238,243,263,253,258,24,210,23,21,22,20,278,268,273,298,283,288,293,97,233,95,96,94,163,153,158,178,168,173,33,32,31,35,220,34,368,341,333,345,359,363,353,335,378,373,191,186,180,200,205,195,131,122,125,145,135,140,47,48,46,217,50,49,57,58,56,60,225,59,317,312,314,310,306,308,245,235,240,261,251,256,44,212,43,45,42,41,275,266,270,297,280,287,290,11,231,10,9,66,161,151,156,175,165,170,52,51,53,54,222,55,365,342,330,347,356,361,350,337,376,370,194,189,184,204,209,199,133,124,129,149,139,144,105,103,104,219,106,107,111,112,115,114,229,113,318,319,320,321,322,323,249,239,244,264,254,259,102,214,101,99,100,98,279,269,274,299,284,289,294,118,234,117,116,119,164,154,159,179,169,174,110,3,2,109,224,108,369,344,334,349,358,364,354,339,379,374,190,185,181,201,206,196,130,121,126,146,136,141,28,26,27,215,29,30,39,40,61,37,226,38,304,305,303,300,302,301,246,236,241,260,250,255,25,211,12,13,14,15,276,265,271,296,281,286,291,65,230,64,62,63,160,150,155,176,166,171,17,16,36,19,221,18,366,340,331,346,355,360,351,336,375,371 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, 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#dba6afe67f86b36e533f777300b41b8ae8b2a840d4529c92a6cd7ab996e48d4f, M = {68} 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, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:45:22 · history